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A right cone has a base with a circumference of 16*pi inches and a height of 80 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.

 Dec 6, 2020
 #1
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Radius of cone

16pi = 2pi r   

r = 8

 

192 pi  =  (1/3) pi  8^2  ( new height)

 

192  = 64/3  * (new height)

 

192 * 3 /64   =  new height

 

(192/64) * 3   = new height

 

9 in =   new height

 

Ratio  =   9  / 80  

 

 

cool cool cool

 Dec 7, 2020

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