<p>For any cube, if the volume is V cubic inches and the surface area is A square inches, then V is directly proportional to which of the following:
(a) A
(b) A^2
(c) A^3
(d) A^2/3
(e) A^3/2</p>
<p>It's E</p>
<p>Well, it’s designed to look hard but if you look at the answers it isn’t .
My logic :</p>
<p>square inches are marked with 2 , cube inches are marked with 3. Since this is a proportion, then they should be either 2/3 or 3/2. And this is where my logic ends. I’d guess between these two.</p>
<p>I think the question is poorly worded. The question assumes that “surface area” only refers to one face of the cube(a square).</p>
<p>Volume is V cubic inches. = each side equals V^(1/3)
Surface Area is A square inches = Each side equal A^(1/2)</p>
<p>V^(1/3) = A^(1/2); cube both sides</p>
<p>V = A^(3/2)</p>
<p>^^this makes no sense in so many ways. one side of a cube has no volume. </p>
<p>When dealing with proportions all constants drop out. V= s^3. SA = 6s^2. (s^3)/(s^2)= s. So, V = SA times s. (s^2)^3/2 = V</p>
<p>Thanks JefferyJung. I see your point, but I thought it meant all sides and D was the closest answer when I plug in random numbers.</p>
<p>Jhannel88, I don’t understand what you mean? Because if you solve this: (s^2)^3/2 = V , doesn’t it equal s^3</p>
<p>Dorky, remember to use google search on THIS site. Plug the question in and you will find previous threads where this has been debated ad nauseam.</p>
<p><a href=“http://talk.collegeconfidential.com/sat-act-tests-test-preparation/1222250-i-cant-get-hard-sat-math-problem.html[/url]”>http://talk.collegeconfidential.com/sat-act-tests-test-preparation/1222250-i-cant-get-hard-sat-math-problem.html</a></p>
<p><a href=“http://talk.collegeconfidential.com/sat-preparation/1179227-need-help-math-problem.html[/url]”>http://talk.collegeconfidential.com/sat-preparation/1179227-need-help-math-problem.html</a></p>
<p>Xiggi, I usually type half the problem into google and if nothing appears, I post the question. And aldfig0, thank you for the links</p>
<p>Assume that one side of the figure is x.</p>
<p>Volume = x^3
SA = 6x^2</p>
<p>Direct proportion is when V = k(SA) where k is a constant. Note that we don’t care about what the constant is.
x^3 = (kx^2)^(_)?</p>
<p>Well, we know that when you have (n^x)^y = n^(xy).
For what value y is x^3 = (x^2)^y?
3 = 2 * y
y = 3/2</p>
<p>Therefore A^3/2 makes the two proportional.</p>
<p>In a cube, all sides are same length… so all faces are squares! </p>
<p>It says surface area is A… now to find the length we find square root of A… to find volume now we take the square root of A and multiply it by square root of A and AGAIN multiply square root of A</p>
<p>Now replace the A with any number who’s square root is a NON decimal number. I will use 16 as an example… square root of a surface area of 16 is (√16) or aka 4… now you know each side is (√16) or 4… now the volume you find of a cube is l<em>b</em>h… (√16)(√16)(√16) OR 4<em>4</em>4… 64 right </p>
<p>so proportions between A to V</p>
<p>A = 16
V = 64</p>
<p>A^x = V
16^x=64</p>
<p>solving for x gives 1.5 or 3/2! :D</p>
<p>you can use any square number like 9,16,25,36,49,64,81 and on and on.</p>
<p>Agree with the other posters: Poorly worded question.</p>
<p>Usually when one has two “variable quantities” (i.e. functions of the same variable) f and g, one says that “f is directly proportional to g” if there is some constant c such that f(s) = c imes g(s) for all s (the input variable). </p>
<p>So in this case…</p>
<p>[imgur:</a> the simple image sharer](<a href=“http://imgur.com/j2Y93]imgur:”>Imgur: The magic of the Internet)</p>
<p>Hope that helps!</p>
<p>It wasn’t that hard btw. It was a,b or c because it said if V=? meaning the the ^3 have to go somewhere. I couldn’t figure out that it was E though.</p>