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A right cone has a base with a circumference of $16\pi$ inches and a height of 30 inches. The height of this cone is reduced while the circumference stays the same. The volume of the shorter cone is $192\pi$ cubic inches. What is the ratio of the shorter height to the original height? Express your answer as a common fraction.

 Jul 5, 2018

V =Pi x r^2 x h/3

Circumference =Radius x 2 x pi

16 pi =Radius x 2 x pi

Radius = 8 inches 

V =Pi x r^2 x h/3

192 pi = pi x 8^2 x h/3, solve for h

h = 9 inches - the shorter height.

The ratio is 9 : 30 = 9/30 = 3/10

 Jul 5, 2018

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