1992 AMC 8 Problem 16

Below is the professionally curated solution for Problem 16 of the 1992 AMC 8, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1992 AMC 8 solutions, or check the answer key.

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Concepts:cylinder volume

Difficulty rating: 980

16.

Which cylinder has twice the volume of the cylinder shown at right?

None of the above

Solution:

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 .

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