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A right cylinder with a base radius of 3 units is inscribed in a sphere of radius 5 units. The total volume, in cubic units, of the space inside the sphere and outside the cylinder is W*pi. Find W, as a common fraction.

 Oct 17, 2018
 #1
avatar+98197 
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Sphere volume =  (4/3) pi (5)^3   =  500/3  pi

 

(1/2) the height of the cylinder is given by  sqrt  [ 5^2 - 3^2 ] = sqrt (16)  = 4

So....the total  height  = 8

 

Cylinder volume  = pi * (3^2) * ( 8)  =  72 pi

 

Volume outside the cylinder but inside the sphere  =  pi [ 500 / 3 - 72 ]  =

 

[ 500 - 216 ] / 3  * pi   =  [284/3] pi

 

So  W  =   284 / 3

 

cool cool cool

 Oct 17, 2018
 #2
avatar+464 
+1

Thank you Chris

 Oct 17, 2018

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