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a cylinder and a cone have the same height, but the base radius of the cylinder is only half of that cone. If the volume of the cylinder is 1, then what is the volume of the cone?

 May 22, 2021
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Let  h  =  the  height of  both

Let  the  radius of the cylinder  =  R    and  that of the  cone =  2R

 

So   for the cylinder

 

1  = pi * R^2  * h

 

And  for the cone

 

V = (1/3) pi ( 2R)^2 *h    =   (1/3)pi  * (4 R^2) * h   =  (4/3) pi R^2 *h

 

But

 

pi R^2 * h  =  1

 

So....the volume of  the  cone  = 

 

(4/3) (1)  =    4/3

 

 

cool cool cool

 May 22, 2021

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