<p>For any cube, if the volume is V cubic inches and the surface area is is A square inches,then V is directly proportional to which of the following?</p>
<p>A. A
B. A^2
C. A^3
D. A ^2/3
E. A ^ 3/2</p>
<p><a href=“http://talk.collegeconfidential.com/sat-preparation/1143340-may-sat-2011-math-section.html?[/url]”>http://talk.collegeconfidential.com/sat-preparation/1143340-may-sat-2011-math-section.html?</a></p>
<p>PS The answer is E.</p>
<p>V=x^3
A=6x^2</p>
<p>Solving the second equation for x yields x= (A/6)^(1/2)</p>
<p>So V = (A/6)^(3/2) and the answer is (E).</p>
<p>Sorry for the two week bump, but I have a stupid question…</p>
<p>Since this problem apparently states that the Volume of a cube is equal to the Surface area raised to the (3/2) power, why does that not hold true when I plug in numbers? </p>
<p>I understand DrSteve’s solution, but let’s say you have a cube with side 3. Volume therefore =27 and surface area = 54. But shouldn’t we be able to take 27^(3/2) and get 54? It doesn’t, it equals 140.30.</p>
<p>I know this is probably a stupid question, but my brain is fried from doing 8 hours of SAT work today, can someone please explain really quick?</p>
<p>That’s because “someone” is mixing the total surface area of a cube and the surface of one face. </p>
<p>9 ^3/2 = 27 :)</p>
<p>oops! I forgot to divide by 6. thanks xig!</p>
<p>Why don’t people just make up a side for 2 cubes and go from there. All you have to do is test out the answer by setting up a proportion between the 2 cubes’ values and see if they’re proportional.</p>
<p>how i dont understand that?</p>
<p>why is there 6</p>
<p>can anyone explain this question to me? i am so puzzled…</p>
<p>@DrSteve, if your equation contains A/6 ^ 3/2, how is the answer E if it doesn’t contain the /6 part?</p>
<p>bump? i keep confusing myself T_T</p>
<p>Hey,.
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Well, I don’t know whether I’ve gone for the right subject choice. I basically want to go to IVY’s league, or probably a renowned university that ACTUALLY polishes my skills, and gives scholarships too. But, I DON’T KNOW WHAT TO DO? THE ROAD MAP? I don’t know whether my subjects are of scope or not. Which university should I apply to? What should I do in future that earns me a comfortable living, and is prestigious too. I’m afraid because I’ve seen many who work extraordinarily hard but they end up living a miserable life.
Here in Pakistan, we lack counselling. Please help me with sound pieces of advices so that I come out of this mental stress.
God bless you.</p>
<p><em>bump</em>
I’m kinda braindamaged today…
I understand the algebraic solution to this problem. But I’d never solve a problem algebraically when I can just plug in some numbers and try out solutions.
Can someone please expound on jd989898’s objection?
Say we have a cube with a side 3.
V = 27
A = 54</p>
<p>So when I take 54^2, I, naturally, don’t come to 27. Ok, I have to take the surface area of one face, 9. Then it fits. But how do I know that I have to take the surface area of one face? The problem says nothing about that. The way it is written, it means that the surface area of the cube (6x^2)^3/2 must be proportional to the cube’s volume. And not the surface area of one of the cube’s faces…</p>
<p>Sry if the question is too dumb. :D</p>
<p>If you are going to use made up numbers to investigate a type of proportion (which is fine, though not as fast as algebra) here’s the thing: you have to make up TWO sets of data so that you can see whether RATIOS are the same.</p>
<p>So yes: side 3 gives V=27 and A=54</p>
<p>Now try side 4: V=64 and A=96</p>
<p>Now that you have two pairs, you can use trial and error on the answer choices. For example, if you were checking if ‘c’ was the right answer:
Is 27/64 = 54^3/96^3 ? No.</p>
<p>When you get to e)…</p>
<p>Is 27/64 = 54^(3/2)/96^(3/2) ? Yes. Yes it is.</p>
<p>Again, this is not the fastest way. But it also explains why the various constants don’t matter – they “drop out” of the ratios.</p>
<p>@Fat Nerd</p>
<p>Sorry - I somehow missed your question until now.</p>
<p>y directly proportional to x means y=kx for some constant k. k is called the constant of proportionality. In the solution here, the constant of proportionality turns out to be (1/6)^(3/2).</p>
<p>So we can say that two expressions are directly proportional with each other without mentioning the constant of proportionality.</p>
<p>Hope this answers your question.</p>