1992 AMC 8 第 16 题

The volume of a cylinder is $\pi r^2 h$; first compute the volume of the given cylinder

Doubling the height doubles the volume, but doubling the radius multiplies the volume by $4$; check the $r$ and $h$ labels on each choice

The given cylinder has volume $\pi \times 10^2 \times 5 = 500\pi,$ so a cylinder of twice the volume has volume $1000\pi.$

The choices have volumes $\pi \times 20^2 \times 5 = 2000\pi$ (A), $\pi \times 10^2 \times 10 = 1000\pi$ (B), $\pi \times 5^2 \times 20 = 500\pi$ (C), and $\pi \times 20^2 \times 10 = 4000\pi$ (D). Only (B) equals $1000\pi.$

Thus, the correct answer is B .