SOLUTION: Cylinder A has the same volume as cylinder B. If the radius of A is three times the radius of B, what is the ratio of the height of A to the height of B?

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Question 1151142: Cylinder A has the same volume as cylinder B. If the radius of A is three times the radius of B, what is the ratio of the height of A to the height of B?
Answer by greenestamps(13216) About Me  (Show Source):
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Let r be the radius of cylinder B; then the radius of cylinder A is 3r.

The volume of cylinder B is %28pi%29%28r%5E2%29%28h%29.

The volume of cylinder A is %28pi%29%28%283r%29%5E2%29%28h%29+=+9%28pi%29%28r%5E2%29%28h%29.

So tripling the radius in cylinder A makes the volume 9 times the volume of cylinder B. If the volumes are to be the same, the height of cylinder A must be 1/9 the height of cylinder B.

ANSWER: The ratio of the heights of cylinders A and B is 1:9.