<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>not sure if i understand this correctly... does anyone mind explaining?</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>@Jeffrey, let’s assume now.</p>
<p>Cube has side 3. Therefore, volume = 27. Therefore, surface area = 54.</p>
<p>Now, using your equation of V = A^3/2, we’ll apply it to 54. </p>
<p>54 ^ 3/2 = 396.81</p>
<p>Shouldn’t it give a result of 27?</p>
<p>@SirWanksalot</p>
<p>Your logic is correct.
However, </p>
<p>Question states that " V is directly proportional to which… "
What happened to constant K?</p>
<p>
</p>
<p>Since the same constant k would be multiplied by all 5 choices, the question writers probably removed the constant of proportionality to eliminate any confusion/ambiguity.</p>
<p>@SirWankalot
I assumed that the surface area only referred to only one side of the cube.</p>