Content or Function Word Pronunciation Practice

You can improve your pronunciation by identifying which words are content words and which words are function words. Content words include main verbs, nouns, adjectives, and adverbs. Function words are necessary for grammar, but do not receive stress in spoken English. Use these exercises to help you learn how to use content and function words to help you with your pronunciation because English is a time-stressed language. In other words, the rhythm and music of English comes from stressing content words. Once youve mastered this exercise, move on to finding focus words to help you further.   Content or Function Word? First, you need to be able to immediately distinguish between content and function words. Write down C for content and F for function.   Example: magazine (C) as (F) many (F) went  with  just  quickly  the  hard  next to  CD ROM  open  had  or  information  in order to  difficult  much  exacting  in front of  Jackhe  however   Answers contentfunctionfunctioncontentfunctioncontentfunctioncontentcontentfunction or content (if helping verb - function / if main verb - content)functioncontentfunctioncontentfunctioncontentfunctioncontentfunctioncontent Content or Function? Stressed or Non-stressed? Next, take a look at the sentences and mark the words that should be stressed. Once you have decided, click on the arrow to see if you have chosen the correct words. Example: Jack (yes) went (yes) to the shop (yes) to grab (yes) some coke (yes). He had finished breakfast before I arrived.  Phillip ordered a huge steak for dinner.  They will have to stay up late if they are going to finish their homework.  It must have been something in the air that caused Jack to shout.  Could you please be more quiet?  Unfortunately, Jack wasnt able to finish on time.  As soon as he has collected the results he will post them to his website.  Peter bought shoes today.There should have been some replies by now.  Knowledge creates opportunities where none have existed before. Answers stressed content words: finished, breakfast, arrived / non-stressed function words: he, had, before, Istressed content words: Phillip, ordered, huge, steak, dinner / non-stressed function words: a, forstressed content words: stay up, late, finish, homework / non-stressed function words: they, will, have to, if, they, are going to, theirstressed content words: something, air, caused, Jack, shout / non-stressed function words: it, must have been, in, the, that, to  stressed content words: please, more, quiet / non-stressed function words: could, you, bestressed content words: unfortunately, Jack, finish, time / non-stressed function words: wasnt able to, onstressed content words: soon, collected, results, post, website / non-stressed function words: as, he, has, the, he, will, them, to, hisstressed content words: Peter, bought, shoes, today / non-stressed function words: 0stressed content words: some, replies, now / non-stressed function words: There should have been, bystressed cont ent words: knowledge, creates, opportunities, none, existed, before / non-stressed function words: where, have Notice how some of the shorter sentences actually have more stressed words than the longer ones (2 compared to 3). These shorter sentences can often take longer to speak than longer sentences with many function words. The Music of English English is a very rhythmic language because of this tendency to accent only certain words. For this reason, you should practice using your ear as much as possible. Often repeating spoken English without looking at the written sentence can also help you learn this music of the language.   Helping Yourself Improve Pronunciation  at Home Finally, practice speaking through the sentences below. First speak the sentence trying to carefully pronounce EVERY word. Notice how unnatural this sounds (as in the listening exercise above showing the contrast between this unnatural pronunciation and the natural way of speaking). Next, focus on speaking the sentences only working on stressing the content words. Tape yourself doing this and you will be surprised at how quickly your pronunciation improves! He drove to work after he had finished working in the garden.Youll find the apples next to the oranges on the shelf over there.Maggie must have been visiting her aunt in Springtown last weekend.Could you pass me the mustard, please?They have been considering buying a new car as soon as they have saved enough money. Teachers can use this lesson plan to help students focus on stress-timed pronunciation in class.

Essay on T.S. Eliot Poetry Analysis - 1597 Words

Till Human Voices Wake Us:and We Drown Analysis of T.S. Eliots Poem â€Å"The Love Song of J. Alfred Prufrock† and Till Human Voices Wake Us T.S. Eliots â€Å"The Love Song of J. Alfred Prufrock† embodies many of the different feelings of Americans during the Modernist movement. Prufrock was seen as the prototype of the modern man, it is through his character in this poem that T.S. Eliot shows how man felt insecure, how the new theories of psychology were changing the concept of the mind and how society was becoming more doubtful and indecisive and less of an action taking people. The film Till Human Voices Wake Us, uses Eliots poem as a base to showcase these ideas and to show how dreams and the past can help shape a man. . Prufrock is†¦show more content†¦He says I instead of we or mentioning he walked with someone. He is also showing that he is not the only lonely man in the city. There are lonely men, more than one, hanging out of windows, as if they are waiting for someone to come by, someon e to spend time with, someone to share their own insecurities with. This idea of loneliness is similar in the movie, Ruby shows up also alone. She doesnt know where she belongs, and has no one in her life. Both Ruby and Sam are forced to interact with one another and face their loneliness. Prufrocks insecurities showcased as he doubts what he is capable of. In lines 81 through 86 he again says I, showing it was him alone, and he talks about how his bald head is brought on a platter. Eliot, who loved to reference the past, is alluding to the story of John the Baptists beheading. Prufrock goes on to say, â€Å"I am no prophet- and heres no great matter;†(83) He is implying that he is not as important, and his moment of greatness is just a â€Å"flicker†(84) and in the moment he was afraid. His fear emphasizes his feeling of inadequacy, by comparing it to the greatness of John the Baptist. He is once more showing how much self doubt he has, he does not believe himself t o be a great man or capable of great things. Sam also looks to the past and it emphasizes his insecurities. He is constantly remembering theShow MoreRelatedThe Era Of Modernism : What People Do People Perceive Through Their Perceptions?945 Words   |  4 Pagesyears of Modernism, T.S. Eliot, Virginia Woolf, and Dylan Thomas established the foundations for modern literature, defining Modernism for the world. Although Modernism is very difficult to define and pinpoint, the Modern writers in England certainty changed the age with their writing. While there were many famous writers of the time, a very distinct and powerful writers was T.S. Eliot. Thomas Stearns Eliot was born in St. Louis, Missouri (Greenblatt 1298). Although T.S. Eliot was born in the UnitedRead MoreTradition And The Individual Talent944 Words   |  4 Pagesand critic T.S. Eliot believes tradition in a poetry sense varies through cultures, through time, and it is ever changing. In Eliot’s critical analysis â€Å"Tradition and the Individual Talent† tradition is something considered passed down but in a poetry sense, it is something that is not inherited, it is something that requires great ambition and focus to learn from past poets. A great poet must learn from predecessors of the difficult art before he or she takes to writing great poetry. According toRead MoreAnalysis of The Hollow Men by T.S. Eliot Ess ay1367 Words   |  6 PagesAnalysis of The Hollow Men by T.S. Eliot Eliot, a master of the written craft, carefully thought out each aspect of his 1925 poem The Hollow Men. Many differences in interpretation exist for Eliots complex poetry. One issue never debated is the extensive range of things to consider in his TS Eliots writing. Because TS Eliot often intertwined his writing by having one piece relate to another The Hollow Men is sometimes considered a mere appendage to The Waste Land. The Hollow MenRead MoreCritical Analysis : The Love Song Of J. Alfred Prufrock895 Words   |  4 PagesEssay Two- Critical Analysis Writing a critical analysis is diving into the text. Readers must break down all parts of the text and pin pointing the author s purpose for the writing. A very challenging poem to analysis is T.S. Eliot’s â€Å"The Love Song of J. Alfred Prufrock†. It has been declared that â€Å"The Love Song of J. Alfred Prufrock† started that Anglo-American modernist movement with poetry. The poem was the first poem with American poetry to flow free verse. At the time, it was deemedRead MoreThe Love Song of J. Alfred Prufrock Essay1524 Words   |  7 Pageshistorical context of a particular poem Poem: T. S. Eliot, ‘The Love Song of J. Alfred Prufrock The context of any given text whether poetry, novels or a movie is always integral to its understanding. Social and historical context of not only the given text, but the writer’s context and reader’s context play an important role in the interpretation and understanding of the major ideas, issues, values and beliefs within the text. T.S (Thomas Stearns) Eliot was one of the twentieth century’s major poetsRead MoreT.S. Eliots View of the Human Condition in The Hollow Men Essay856 Words   |  4 Pages T. S. Eliot was a man who strongly believed that poetry should represent life. He knew that life was complex, so that is why his poetry was difficult to understand not only for students writing research papers, but also for critics. He was the backbone of modernist poetry, who wrote mostly about darkness, despair, and depression in life. He tried and succeeded to capture the torment of the world during World War 1 and World War II (Shmoop T.S. Eliot). Eliot’s view of the human condition isRead MoreT.S. Eliot the Wasteland Essay1371 Words   |  6 PagesWrite a critical analysis, focusing particularly on what makes your chosen passage a piece of Modernist writing. Unreal City, Under the brown fog of a winter dawn, A crowd flowed over London Bridge, so many, I had not thought death had undone so many. Sighs, short and infrequent, were exhaled, And each man fixed his eyes before his feet. Flowed up the hill and down King William Street, To where Saint Mary Woolnoth kept the hours With a dead sound on the final stroke of nine. There I sawRead MoreAnalysis Of. Eliot s The Four Quartets And `` The Waste Land ``1784 Words   |  8 PagesI. Introduction to T.S Eliot T.S. Eliot wrote poems that communicated his antagonistic perspectives of life, mankind, and his general surroundings by exemplifying and escalating particular angles and analogies in his written work. T.S. Eliot was born in 1888 and lived during early 1900 s and was a part of Modernist Period. He lived throughout two world wars and struggled with poverty and oppression which impacted his writings. Eliot wrote The Four Quartets and The Waste Land which are importantRead MoreAnalysis Of The Poem Cousin Nancy And Morning At The Window Poem Analysis And Exploration1475 Words   |  6 Pages â€Å"Cousin Nancy† and â€Å"Morning at the Window† Poem Analysis and Exploration Cousin Nancy By T. S. Eliot Miss Nancy Ellicott Strode across the hills and broke them, Rode across the hills and broke them — The barren New England hills — Riding to hounds Over the cow-pasture. Miss Nancy Ellicott smoked And danced all the modern dances; And her aunts were not quite sure how they felt about it, But they knew that it was modern. Upon the glazen shelves kept watch MatthewRead MoreEssay about Modernism in T.s. Eliotss the Wasteland885 Words   |  4 PagesModernism in T.S. Eliots The Wasteland Modernism has been defined as a rejection of traditional 19th-century norms, whereby artists, architects, poets and thinkers either altered or abandoned earlier conventions in an attempt to re-envision a society in flux. In literature this included a progression from objectivist optimism to cynical relativism expressed through fragmented free verse containing complex, and often contradictory, allusions, multiple points of view and other poetic devices

Political Theory Comparing Locke, Rousseau and Plato Essay

Locke: What is the purpose of politics - we could live in the state of nature, we don’t need contract or soverign - life, liberty and property State of nature: men live according to reason and governed by reason - man exists in the state of nature in perfect freedom to do as they want, a state of perfect freedom - not necessarily good or bad, bit is calm and peaceful - men give up some of their freedom to secure the advantages of civilized socity - men have the right to protect their freedom (killing if necessary) - bound by the laws of nature - contrast with hobbes: everyone has the right over everything, there exist no private property - Liberty to do as†¦show more content†¦Ã¢â‚¬ ¢ First part says that the aim of the contract is to protect and defend the common goods of each member. Consistent with Locke’s claims that the purpose of society is protect the security of each members. Rousseau adds a second and more disctinctly original claim. †¢ The contract must ensure the conditions for mutual protection, but also in uniting with one another each person obeys only himself and remains as free as he was before. †¢ Isn’t the essence of the social contract giving up part of our natural freedom? †¢ How can we remain as free. †¢ Total alienation of each associate together with all of his rights to the entire community †¢ Total alienation, entire community. †¢ To ensure the terms of the agreements, persons must totally give themselves up for the social contract. †¢ When we alienate ourselves, this must be given to the entire community. This is to ensure that the general will works. †¢ General will is only legitimate sovereign. The famous doctrine of the sovereignty of the people †¢ When we give ourselves over to it, we do nothing more than obey ourselves. Sovereign is not third party, it is simply the people as a whole acting in their collective capacity. †¢ How do we remain as free as we were before? †¢ Formula for freedom or tyranny of the majority? †¢ Only through total alienation do we remain free, because nobody isShow MoreRelatedJurisprudential Theories on IPR13115 Words   |  53 Pagesproperty, such as: 1. Natural Rights/Justice Argument: this argument is based on Locke’s idea that a person has a natural right over the labour and/or products which is produced by his/her body. Appropriating these products is viewed as unjust. Although Locke had never explicitly stated that natural right applied to products of the mind,[34]  it is possible to apply his argument to intellectual property rights, in which it would be unjust for people to misuse anothers ideas.[35]  Lokeans argument for intellectualRead MoreThe Implication of Paulo Freires Banking Concept to the 8.4.4 System of Education in Kenya9634 Words   |  39 Pages The frustrations faced in the efforts placed while going through the 8:4:4 system necessitated this study. This paper will try to find out to what extent the associationism theory of John Locke will be applicable in analyzing how Kenyan education has contributed to lack of creativity in the country. Based on this theory, it is hoped that solutions will be suggested. It’s my position that we go back to the drawing board (in this case, classroom) to re-design our curriculum. There is dire need forRead MoreNormality and Coercion: Plato, Aristotle, Locke, Rousseau, Kant, and Rawls3749 Words   |  15 PagesHobbes theory of the Leviathan replacing the ‘state of nature’, what is his conception of normativity and coercion? Discuss three writers from different disciplines who change and update these conceptions and the relationship between normativity and coercion. The 17th Century English philosopher Thomas Hobbes is now widely regarded as one of a handful of truly great political philosophers, whose masterwork Leviathan rivals in significance the political writings of Plato, Aristotle, Locke, Rousseau

Bare free essay sample

Giggles and sneers. â€Å"Where’re your shoes?†I smile without meaning to and lightheartedly shrug, â€Å"In my backpack. I just felt like taking them off.† Sure, of course walking barefoot seems a little strange—maybe a little too Hippie for this era—but some spring days are just meant to be lived without shoes on. I often find that when bustling around campus, my mind is too busy freaking out about exams, soccer, or the dress I have to finish making to really look where I’m stepping. Today’s emphasis—and probably tomorrow’s—focuses more on where we are supposed to end up, and less on the stones we have to jump on to get there: my first lead role, flying alone to Spain, or my Geometry final freshman year that I stayed up all night to study for. Shoes only encourage this neglect. Shoes enable us to walk blindly because with our feet in a cage of safety, we don’t have to look where we step—we are protected. We will write a custom essay sample on Bare or any similar topic specifically for you Do Not WasteYour Time HIRE WRITER Only 13.90 / page Children run around barefoot all the time despite the frowns of worried parents. I know I stubbed my toe at least ten times as a kid running around suburban streets determined to catch a football—and clearly even after the fifth time I wasn’t afraid of taking the risk of bare feet again. As a seven year old, I swash-buckled with trees and wrote stories that came to me while making fairy houses in the backyard. I didn’t care that trees didn’t fight back, or that my stories didn’t make sense, or even when my fairy houses collapsed. I didn’t worry about failure—I could always try and build that fairy house again another time. That stubbed toe: well, slap a band-aid on it and keep running. Where did all that fearlessness go?Play it safe, do what you know you can do, just get through the day, and wear shoes. Yes, my mature head tells me to be secure and I’ll have a comfortable future. If I walk only â€Å"inside the box† then I won’t have to feel any hurt, any disappointment, and definitely won’t have to feel the sting of a stubbed toe. If I had always lived in a laced up comfort zone I never would have experienced getting cut from the soccer team I tried out for, messing up during a flute concert, or losing my voice as a cabin leader at Outdoor Ed. See though, sometimes we have to take risks, even if the outcome doesn’t always seem worth it. If we never skid through any dirty puddles, we can never know the true taste of victory. Luckily, my heart is a bit more reckless than my head and still believes in writing wild stories and sprinting barefoot.My campus is lettered with painful gravel and gross dirt, not to mention scorching pavement—something I only caught onto once my sandals were in my backpack. Yet as I gratefully stroll over a patch of lawn, I also start to appreciate just how wonderfully soft the grass is, and when I enter the Main building, I enjoy the cool wooden hallway more than I should for just a plain spring day. A grin smears itself into the corner of my mouth and I realize all these things I feel biting or soothing my feet mean I’m alive. It’s all good.

The 108 Most Persuasive Words In The English Language - The Writers For Hire

THE 108 MOST PERSUASIVE WORDS IN THE ENGLISH LANGUAGE It's long known the secret to persuasive writing isn't in the adjectives, it's in the verbs.Tweet this Copywriters know power verbs sell and convince. Internally, we have a list of 108 verbs that weve been using for a good decade, and we recently thought we should share it with proper credit to the original author. We found that although the list is being recirculated (and in many cases claimed as original by several different authors!), the original author is in fact nowhere to be found. If anyone knows who wrote this, wed love to know! With or without the original author, its still a great listhere it is! The 108 Most Persuasive Words In The English Language According to legendary advertising man, Leo Burnet, â€Å"Dull and exaggerated ad copy is due to the excess use of adjectives.† To prove it, he asked his staff to compare the number of adjectives in 62 ads that failed to the number of adjectives in Lincoln’s Gettysburg Address, and other age-old classics. Here’s what he discovered: Of the 12,758 words in the 62 failed ads, 24.1% were adjectives. By direct comparison, Lincoln’s Gettysburg Address contains only 35 adjectives out of 268 immortal words – only 13.1% adjective-to-total-word ratio. Winston Churchill’s famous â€Å"Blood, Seat and Tears† speech rates even lower and has a 12.1% adjective ratio (81 adjectives from 667 words). Mr. Burnett found that similar ratios applied to great works such as The Lord’s Prayer, the Ten Commandments, and the Preamble to the U.S. Constitution. Conclusion: Use more verbs, not adjectives. Verbs increase the pulling-power and believability of ad copy. That’s why it makes sense to keep this 108-VERB â€Å"CHEAT-SHEET close-by whenever you begin to draft your next space ad, sales letter, Website, or email campaign.

Nuturing Charge Nurse Example

Nuturing Charge Nurse Example Nuturing Charge Nurse – Article Example RAPID CRITICAL APPRAISAL CHECKLISTS s From the study, it was found that the question of study was relevant since the question was of high quality regarding the clinician’s practices. Case control studies were also relevant to the study. It involved nurses who had already developed the outcome of interest. Data was then collected concerning the influential factors that led to the outcome. It was qualitative and quantitative test of nurturing charge nurse for future leadership roles. Cohort studies were included in this study and they involved 3 focus groups with experience in working in small hospitals with less than 300 beds. The focus group was similar in size habit with similar background and views. This was aimed at eliminating bias (Patricia A. Patrician, 2012).Randomized clinical trials were done for this study. Conventional content analysis described by Hseih and Shannon theories were used in analyzing the data. There was a clear systematic review of the clinical interve ntions studies since these involved randomly selected nurses. The study design was also appropriate for the research question. The study was having a high degree protection against bias. Moreover, the study addresses the key potential sources of bias. There was sufficient information with regard to qualitative evidence for the study. Most of the conclusion and discussion was drawn from the study. There was a particular standardized protocol use with the systematic review to identity.Evidence based clinical practices were available from the study. This was verified in terms of the roles of the nurses in the management process. ReferencesPatricia A. Patrician, D. O. (2012). Nurturing Charge Nurses for Future. THE JOUR N A L O F NUR S I N G A D M I N I S T R A T I O N , Volume 42, Number 10, pp 461-466.

Solid Geometry on SAT Math The Complete Guide

Solid Geometry on SAT Math The Complete Guide SAT / ACT Prep Online Guides and Tips Geometry is the branch of mathematics that deals with points, lines, shapes, and angles. SAT geometry questions will test your knowledge of the shapes, sizes, and volumes of different figures, as well as their positions in space. 25-30% of SAT Math problemswill involve geometry, depending on the particular test. Because geometry as a wholecovers so many different mathematical concepts, there are several different subsections of geometry (including planar, solid, and coordinate). We will cover each branch of geometryin separate guides, complete with a step-by-step approach to questions and sample problems. This articlewill be your comprehensive guide to solid geometry on the SAT. We’ll take you through the meaning of solid geometry, the formulas and understandings you’ll need to know, and how to tackle some of the most difficult solid geometry problems involving cubes, spheres, and cylinders on the SAT. Before you continue, keep in mind that there will usually only be 1-2 solid geometry questions on any given SAT, so you should prioritize studying planar (flat) geometry and coordinate geometry first. Save learning this guide for last in terms of your SAT math prep. Before you descend into the realm of solid geometry, make sure you are well versed in plane geometry and coordinate geometry! What is Solid Geometry? Solid geometry is the name for geometry performed in three dimensions. It means that another dimension- volume- is added to planar (flat) geometry, which only uses height and length. Instead of flat shapes like circles, squares, and triangles, solid geometry deals with spheres, cubes, and pyramids (along with any other three dimensional shapes).And instead of using perimeter and area to measure flat shapes, solid geometry uses surface area and volume to measure its three dimensional shapes. A circleis a flat object. This is plane geometry. A sphere is a three-dimensional object. This is solid geometry. On the SAT, most of the solid geometry problems are located at the end of each section. This means solid geometry problemsare considered some of the more challenging questions (or ones that will take the longest amount of time, as they often need to be completed in multiple pieces).Use this knowledgeto direct your study-focus to the most productive avenues. If you are getting several questions wrong in the beginning and middle sections of each math section, it might be more productive for you to take the time to first refresh your overall understanding of the math concepts covered by the SAT. You can alsocheck out how to improve your math scoreor refresh your understanding of all the formulas you’ll need. Note: most of the solid geometry SAT Math formulas are given to you on the test, either in the formulas box or on the question itself. If you are unsure which formulas are given or not given in the math section, refresh your formulas knowledge. This is the formula box you'll be given on all SAT math sections. You are given the formulas for both the volume of a rectangular solid and the volume of a cylinder. Other formulas will often be given to you in the question itself. But whilemany of the formulas are given, it is still important for you to understand how they work and why. So don’t worry too much about memorizing them, but do pay attention to them in order to deepen your understanding of the principles behind solid geometry on the SAT. In this guide, I’ve divided the approach to SAT solid geometry into three categories: #1: Typical SAT solid geometry questions #2: Types of geometric solids and their formulas #3: How to solve an SAT solid geometry problem with our SAT math strategies Solid geometry adventure here we come! Typical Solid Geometry Questions on the SAT Before we go through the formulas you'll need to tacklesolid geometry, it's important to familiarize yourself with the kinds of questions the SAT will ask you about solids. SAT solid geometry questions will appear in two formats: questions in which you are given adiagram, and word problem questions. No matter the format, each type of SAT solid geometry questionexiststotestyour understanding of the volume and/or surface area of a figure. You will be asked how to find the volume or surface area of a figure or you'll be asked to identify how a shape's dimensions shift and change. Diagram Problems A solid geometry diagram problem will provide you with a drawingof a geometrical solid and ask you to find a missing element of the picture. Sometimes they will ask you to find the volume of the figure, the surface area of the figure, or the distance between two points on the figure. They may alsoask you to compare the volumes, surface areas, or distances of several different figures. This is a typical "comparing solids" SAT question. We'll go through how to solve it later in the guide. Word Problems Solid geometry word problemswill usually ask you tocomparethe surface areas or volumes of two shapes. They will often giveyou the dimensions of one solid and then tell youto compare its volume or surface area to a solid with different dimensions. By how many cubic feet is a box with a height of 2inches, a width of 6 inches, and a depth of 1 inch greater than a cylinder with a height of 4 inches and a diameter of 6 inches? This is a typical word problem question that might appear in the grid-in section of the SAT math Other word problems mightask you to contain one shape within another. This is just another way of getting you to think about a shape's volume and ways to measure it. What is the minimum possible volume of acube, in cubic inches,thatcouldinscribe a sphere with a radius of 3 inches? A) $12√3$ (approximately $20.78$) B) $24√3$ (approximately $41.57$) C) $36√3$ (approximately $62.35$) D) $216$ E)$1728$ This is a typical inscribing solids word problem. We'll go through how to solve it later in the guide. Solid geometry word problemscan be confusing to many people, because it can be difficult to visualize the question without apicture. As always with word problems that describe shapes or angles, make the drawing yourself! Simplybeing able to seewhat a question is describing can do wonders to help clarify the question. Overall Style of Solid Geometry Questions Every solid geometry question on the SAT is concerned with either the volume or surface area of a figure, or the distance between two points on a figure. Sometimes you'll have to combine surface area and volume, sometimes you'll have to compare two solids to one another, but ultimately all solid geometry questions boil down to these concepts. So now let's go through how to find volumes, surface areas, and distances of all the different geometric solids on the SAT. A perfect example of geometric solidsin the wild Prisms A prism is a three dimensional shape that has (at least) two congruent, parallel bases. Basically, you could pick up a prism and carry it with its opposite sides lying flat against your palms. A few of the many different kinds of prisms. Rectangular Solids A rectangular solid is essentially a box. It has three pairs of opposite sides that are congruent and parallel. Volume $\Volume = lwh$ The volume of a figure is the measure of its interior space. $l$ is the length of the figure $w$ is the width of the figure $h$ is the height of the figure Notice how this formula is the same as findingthe area of the square ($A = lw$) with the added dimension of height, as this is a three dimensional figure First, identify the type of question- is it asking for volume or surface area? The question asks about the interior space of a solid, so it's a volume question. Now we need to finda rectangular volume, but this question is somewhat tricky. Notice that we're finding out how much water is in a particular fish tank, but the water does not fill up the entire tank. If we just focus on the water, we would find that it has a volume of: $V = lwh$ = $(4)(3)(1) = 12\cubic\feet$ (Why did we multiply the feet and width by 1 instead of 2? Because the water only comes up to 1 foot; it does not fill up the entire 2 feet of height of the tank) Nowwe are going to put that 12 cubic feet of water into a second tank. This second tank has a total volume of: $V = lwh$ = $(3)(2)(4) = 24\cubic\feet$ Although the second tank can hold 24 cubic feet of water, we are only putting in 12. So $12/24 = 1/2$. The water will come up at exactly half the height of the second tank, which means the answer is D, 2 feet. Either way, those fish won't be very happy in half a tank of water Surface Area $\Surface\area = 2lw + 2lh + 2wh$ In order to find the surface area of a rectangular prism, you are finding the areas for all the flat rectangles on the surface of the figure (the faces) and then adding those areas together. In a rectangular solid, there are six faces on the outside of the figure. They are divided into three congruent pairs of opposite sides. If you find it difficult to picture surface area, remember that a die has six sides. So you are finding the areas of the three combinations of length, width, and height (lw, lh, and wh), which you then multiply by two because there are two sides for each of these combinations.The resulting areas are then all added together to getthe surface area. Diagonal Length $\Diagonal = √[l^2 + w^2 + h^2]$ The diagonal of a rectangular solid is the longest interior line ofthe solid. It touches from the corner of one side of the prismto the opposite corner on the other. You can find this diagonal by either using the above formula or by breaking up the figure into two flat triangles and using the Pythagorean Theorem for both. You can always do this is you do not want to memorize the formula or if you're afraid of mis-remembering the formula on test day. First, find the length of the diagonal (hypotenuse) of the base of the solid using the Pythagorean Theorem. $c^2 = l^2 + w^2$ Next, use that length as one of the smaller sides of a new triangle with the diagonal of the rectangular solid as the new hypotenuse. $d^2 = c^2 + h^2$ And solve for the diagonal using the Pythagorean Theorem again. Cubes Cubes are a special type of rectangular solid, just like squares are a special type of rectangle A cubehasa height, length, and width that are all equal. The six faces on a cube's surface are also all congruent. Volume $\Volume = s^3$ $s$ is the length of the side of a cube (any side of the cube, as they are all the same). This is the same thing as finding the volume of a rectangular solid ($v = lwh$), but, because their sides are all equal, you can simplify it by saying $s^3$. First, identify what the question is asking you to do. You're trying to fit smallerrectangles into a larger rectangle, so you're dealing with volume, not surface area. Find the volume of the larger rectangle (which in this case is a cube): So you can use the formula for the volume of a cube: $\Volume = s^3$ = $6^3 = 216$ Or you can use the formula to find the volume of any rectangular solid: $\Volume = lwh$ = $(6)(6)(6) = 216$ Now find the volume of one of the smaller rectangular solids: $\Volume = lwh$ = $(3)(2)(1) = 6$ And divide the larger rectangular solid by the smaller to find out how many of the smaller rectangular solids can fit inside the larger: $216/6 = 36$ So your final answer is D, 36 SurfaceArea $\Surface\area = 6s^2$ This is the same formulas as the surface area for a rectangular solid ($SA = 2lw + 2lh + 2hw$). Because all the sides are the same in a cube, you can see how $6s^2$ was derived: $2lw + 2lh + 2hw$ = $2ss + 2ss + 2ss$ = $2s^2 + 2s^2 + 2s^2$ = $6s^2$ Diagonal Length $\Diagonal= s√3$ Just as with the rectangular solid, you can break up the cube into two flat triangles and use the Pythagorean Theorem for both as an alternative to the formula. This is the exact same process as finding the diagonal of a rectangular solid. First, find the length of the diagonal (hypotenuse) of the base of the solid using the Pythagorean Theorem. Next, use that length as one of the smaller sides of a new triangle with the diagonal of the rectangular solid as the new hypotenuse. Solve for the diagonal using the Pythagorean Theorem again. Cylinders A cylinder is a prism with two circular bases on its opposite sides Notice how this problem only requires you to know that thebasic shape of a cylinder.Draw out the figure they are describing. If the diameter of its circular bases are 4, that means its radius is 2. Now we have two side lengths of a right triangle. Use the Pythagorean Theorem to find the length of the hypotenuse. $2^2 + 5^2 = c^2$ = $29 = c^2$ = $c = √29$, or answer C Volume $\Volume = πr^2h$ $π$ is the universal constant, also represented as 3.14(159) $r$ is the radius of the circular base. It is any straight line drawn from the center of the circle to the circumference of the circle. $h$ is the height of the circle. It is the straight line drawn connecting the two circular bases. This problem requires you to understand how to get both the volume of a rectangular solid and the volume of a cylinder in order to compare them. A right circular cylinder with a radius of 2 and a height of 4 will have a volume of: $V = πr^2h$ = $π(2^2)(4) = 16π$ or $50.27$ The volumes for the rectuangular solids are found by: $V = lwh$ So solid A has a volume of $(3)(3)(3) = 27$ Solid B has a volume of $(4)(3)(3) = 36$ Solid C has a volume of $(5)(4)(3) = 60$ Solid D has a volume of $(4)(4)(4) = 64$ And solid E has a volume of $(4)(4)(3) = 48$ So the answer is E, 48 Surface Area $\Surface\area = 2πr^2 +2πrh$ To find the surface area of a cylinder, you are adding the volume of the two circular bases ($2πr^2$), plus the surface of the tube as if it were unrolled ($2πrh$). The surface of the tube can also be written as $SA = πdh$, because the diameter is twice the radius. In other words, the surface of the tube is the formula for the circumference of a circle with the additional dimension of height. Non-Prism Solids Non-prism solids are shapes in three dimensions that do not have any parallel, congruent sides. If you picked these shapes up with your hand, a maximum ofone side (if any) would lie flat against your palm. Cones A cone is similar to a cylinder, but has only one circular base instead of two. Its opposite end terminates in a point, rather than a circle. There are two kind of cones- right cones and oblique cones. For the purposes of the SAT, you only have to concern yourself with right cones. Oblique cones are restricted to the math I and II subject tests. A right cone has an apex (the terminating point on top) that sits directly above the center of the cone’s circular base. When a height ($h$) is dropped from the apex to the center of the circle, it makes a right angle with the circular base. Volume $\Volume = 1/3πr^2h$ $π$ is a constant, written as 3.14(159) $r$ is the radius of the circular base $h$ is the height, drawn at a right angle from the cone’s apex to the center of the circular base The volume of a cone is $1/3$ the volume of a cylinder. This makes sense logically, as a cone is basically a cylinder with one base collapsed into a point. So a cone’s volume will be less than that of a cylinder. Surface Area $\Surface\area = πr^2 + pirl$ $l$ is the length of the side of the cone extending from the apex to the circumference of the circular base The surface area is the combination of the area of the circular base ($πr^2$) and the lateral surface area ($πrl$) Because right cones make a right triangle with side lengths of: $h$, $l$, and $r$, you can often use the pythagorean theorem to solve problems. Pyramids Pyramids are geometric solids that are similar to cones, except that they have a polygon for a base and flat, triangular sides that meet at an apex. There are many types of pyramids, defined by the shape of their base and the angle of their apex, but for the sake of the SAT, you only need to concern yourself with right, square pyramids. A right, square pyramid has a square base (each side has an equal length) and an apex directly above the center of the base. The height ($h$), drawn from the apex to the center of the base, makes a right angle with the base. Volume $\Volume = 1/3\area\of\the\base * h$To find the volume of a square pyramid, you could also say $1/3lwh$ or $1/3s^2h$, as the base is a square, so each side length is the same. Spheres A sphere is essentially a 3D circle. In a circle, any straight line drawn from the center to any point on the circumference will all be equidistant. This distance is the radius (r). In a sphere, this radius can extend in three dimensions, so all lines from the surface of the sphere to the center of the sphere are equidistant. Volume $\Volume = 4/3πr^3$ Inscribed Solids The most common inscribed solids on the SAT will be: cube inside a sphere and sphere inside a cube. You may get another shape entirely, but the basic principles of dealing with inscribed shapes will still apply. The question is most often a test ofYou’ll often have to know the solid geometry principles and formulas for each shape individually to be able to put them together. When dealing with inscribed shapes, draw on the diagram they give you. If they don’t give you a diagram, make your own!By drawing in your own lines, you’ll be better able to translate the three dimensional objects into a series of two dimensional objects, which will more often than not lead you to your solution. Understand that when you are given a solid inside another solid, it is for a reason. It may look confusing to you, but the SAT will always give you enough information to solve a problem. For example, the same line will have a different meaning for each shape, and this is often the key to solving the problem. So we have an inscribed solid and no drawing. So first thing's first, make your drawing! Now because we have a sphere inside a cube, you can see that the radius of the sphereis always half the length of any side of the cube (because a cube by definition has all equal sides). So $2r$ is the length of all the sides of the cube. Now plug $2r$ into your formula for finding the volume of a cube. You can either use the cube volume formula: $V = s^3$ = $(2r)^3 = 8r^3$ Or you can use the formula to find the volume of any rectangular solid: $V = lwh$ = $(2r)(2r)(2r) = 8r^3$ Either way, you getthe answer E,$8r^3$ Notice how answer B is $2r^3$. This is a trick answer designed to trap you. If you didn't use parentheses properly in your volume of a cube formula, you would have gotten $2r^3$. But if you understand that each side length is $2r$ and so that entire length must be cubed, then you will get the correct answer of $8r^3$. For the vast majority of inscribed solids questions, the radius (or diameter) of thecircle will be the key to solving the question.The radiusof the sphere will be equal to half the length of the side of a cube if the cube is inside the sphere (as in the question above). This means that the diameter of the sphere will be equal to one side of the cube, because the diameter is twice the radius.. But what happens when you have a sphere inside a cube? In this case, the diameter of the sphere actually becomes the diagonal of the cube. What is the maximum possible volume of acube, in cubic inches,thatcould be inscribed inside a sphere with a radius of 3 inches? A) $12√3$ (approximately $20.78$) B) $24√3$ (approximately $41.57$) C) $36√3$ (approximately $62.35$) D) $216$ E)$1728$ First, draw out your figure. You can see that, unlike when the sphere was inscribed in the cube, the side of thecube is not twice the radius of the circle because there are gaps between the cube's sides and the circumference of the sphere. The only straight line of the cube that touches two opposite sides of the sphere is the cube's diagonal. So we need the formula for the diagonal of a cube: $\side√3 = \diagonal$ $s√3 = 6$ (Why is the diagonal 6? Because the radius of the sphere is 3, so $(3)(2) = 6$) $3s^2 = 36$ $s^2 = 12$ $s = √12$ $(√12)^3 = 12√12 = 24√3$ Though solid geometry may seem confusing at first,practice and attention to detail will have you navigating the way to the correct answer The Take-Aways The solid geometry questions on the SAT will alwaysask you about volume, surface area, or the distance between points on the figure. The way they make it tricky is by making you compare the elements of different figures or by making you take multiple steps per problem. But you can always break down any SAT question into smaller pieces. The Steps to Solvinga Solid Geometry Problem #1: Identify what the problem is asking you to find. Is the problem asking about cubes or spheres? Both? Are you being asked to find the volume or the surface area of a figure? Both? Make sure you understandwhich formulas you'll need and what elements of the geometric solid(s) you are dealing with. #2: Draw it out Draw a picture any time they describe a solid without providing you with a picture. This will often make it easier to see exactly what information you have and how you can use that information to find what the question is asking you to provide. #3: Use your formulas Once you've identified the formulas you'll need, it's often a simple matter of plugging in your given information. If you cannot remember your formulas (like the formula for a diagonal, for example), use alternative methods to come to the answer, like the pythagorean theorem. #4: Keep your information clear and double check your work Did you make sure to label your work? The makers of the test know that it's easy for students to get sloppy in a high-stress environment and they put in bait answers accordingly. So make sure thevolume for your cylinder and thevolume for your cube are labeled accordingly. And don't forget to give your answer a double-check if you have time! Does it make sense to say that a box with a height of 20 feet can fit inside a box with a volume of 15 cubic feet? Definitely not! Make sure all the elements of your answer and your work are in the right place before you finish. Follow the steps to solving your solid geometry problems andyou'll get that gold Solid geometry is often not as complex as it looks; it is simply flat geometry that has been taken into the third dimension. If you can understand how each of these shapes changes and relate to one another, you’ll be able to tackle this section of the SAT with greater ease than ever before. What's Next? Now that you've done your paces onsolid geometry, it might bea good idea to review all the math topics tested on the SAT to make sure you've got them nailed down tight. Want to get a perfect score? Check out our article onHow to an 800 on the SAT Mathby a perfect SAT scorer. Currently scoring in the mid-range? Running out of time on the math section?Look no further than our articles on how to improve your score if you're currently scoring below the 600 rangeand how to stop running out of time on the SAT math. Want to improve your SAT score by 160 points? Check out our best-in-class online SAT prep program. We guarantee your money back if you don't improve your SAT score by 160 points or more. Our program is entirely online, and it customizes what you study to your strengths and weaknesses. If you liked this Math strategy guide, you'll love our program.Along with more detailed lessons, you'll get thousands of SAT Mathpractice problems organized by individual skills so you learn most effectively. We'll also give you a step-by-step program to follow so you'll never be confused about what to study next. Check out our 5-day free trial: