Gruber's SAT Math Refresher Questions!

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1

<p>I've just started working through Gruber's to try to raise my SAT math score but I'm having trouble understanding the solutions to some of the questions I'm getting wrong. I'd really appreciate it if someone can help! Variation is my main problem so far. I understand the explanation in the refresher but don't understand it in a different context. </p>

<ol>
<li>The formula for the volume of a cone is V=(1/3)(pi)(r^2)(h). If the radius is doubled and the height is divided by 3 what will be the ratio of the new volume to the original volume?</li>
</ol>

<p>a) 2:3
b) 3:2
c) 4:3
d) 3:4
e) None of these</p>

<p>I know the answer is C from looking at the solution but I don't understand why.</p>

<p>The furthest I'm getting in the solution is V'=(4/3)(pi)(r^2)(h/3). I don't know where to go from there or even if I'm right so far...</p>

2

<p>The easy way to solve this kind is by plugging in numbers
Say the radius=2 and hight=3
so the volume = (1/3)(pi)(2^2)(3) = 4 Pi</p>

<p>and after doubling the radius and dividing the hight by 3
then the radius = 4 and hight=1
so the volume = (1/3)(pi)(4^2)(1) = 16/3 pi</p>

<p>then finally the ratio between the new volume to the main volume = (16/3 pi)/4 pi = 4/3</p>

3

<p>And now it all makes sense! :P</p>

<p>I didn’t think to plug in some numbers. Thank you for your help.</p>