Question 26·200 Super-Hard SAT Math Questions·Geometry and Trigonometry

Let $k$ be the linear scale factor from A to B: each length in B is $k$ times its match in A. Lateral surface area is the curved outside of a cone; like any area, it changes by $k^2$. Put B's area over A's to match the direction from A to B:

Type $k^2\sim\frac{9}{25}\{k>0\}$ in Desmos. The $\sim$ asks Desmos to find $k$, and the restriction keeps it positive because lengths can't be negative. Under PARAMETERS, Desmos shows $k=0.6$, or $\frac35$.

Cone A's volume is $500\pi$. A volume uses the cube of the same length factor that an area squares. So cube $k$ to get cone B's volume: $V_B=500\pi k^3$. Using $\frac9{25}$ instead would apply an area factor to a volume.

Type $500k^3$ beneath the regression. Desmos shows $108$; that's the number multiplying $\pi$. Cone B's volume is $108\pi$ cubic centimeters. Choice D.