If x = 2, then the cone has radius 2 and height 4.
So what does r have to be for the volumes to be equal?
When x = 2, r turns out to be . Now plug x = 2 into the answer choices. Without too much effort,
you can tell that (A), (C) and (E) are wrong. What about (B) and (D)?
(B)
Rationalize the denominator of (D) in the same way, and of course it doesn’t turn out to be
(since it differs from (B) by a factor of x, or 2, in this case). This alternative method is still somewhat
algebraic, but this way the algebra’s a lot less convoluted.
BRUSH UP ON YOUR ALGEBRA
You can’t escape algebra! The Mathematics subject tests are both full of algebra. Make sure
your algebra skills are in peak condition by Test Day.