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A cylinder and a cone have the same volume. The cylinder has radius x and height y. The cone has radius 3x. Find the height of the cone in terms of y.

 Dec 11, 2021
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Volume(cylinder)  =  pi · radius2 · height  =  pi · radius2 · height  =  pi · x2 · y

 

Volume(cone)  =  (1/3) · pi · radius2 · height  =  (1/3) · pi · (3x)2 · h  =  3 · pi · x2 · h

 

Volume(cylinder)  =  Volume(cone)     --->     pi · x2​ · y  =  3 · pi · x2 · h     --->     h  =  (1/3) · y  

 Dec 11, 2021

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