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A right circular cone is inscribed in a right circular cylinder. The volume of the cylinder is \(72\pi\) cubic centimeters. What is the number of cubic centimeters in the space inside the cylinder but outside the cone? Express your answer in terms of \(\pi\).

 

tertre  Mar 21, 2018
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 #1
avatar+6949 
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Let the height of the cylinder be  H

Let the area of the base of the cylinder be  B

 

volume of cylinder  =  BH  =  72π

 

volume of cone  =  (1/3)BH   =   (1/3)(72π)  =  24π

 

volume of cylinder - volume of cone  =  72π - 24π  =  48π     (cubic centimeters)

hectictar  Mar 21, 2018
 #2
avatar+92225 
+3

A right circular cone is inscribed in a right circular cylinder. The volume of the cylinder is  \(72\pi\)  cubic centimeters. What is the number of cubic centimeters in the space inside the cylinder but outside the cone? Express your answer in terms of .

 

The volume of the cone is 1/3 the volume of the cylinder

so the volume of the cylinder not including the cone is the other 2/3

 

2/3*72 = 48

 

the desired volume is \(48\pi\)    cubic cntimetres

Melody  Mar 21, 2018

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