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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.

 Jan 1, 2019
 #1
avatar+100586 
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Using the Pythagorean Theorem.....the height of 1/2 of the cylinder is

 

√[5^2 - 3^2] = √[16]  =  4

 

So....the height of the whole cylinder =  8 units

 

The space between the sphere and the cylinder is given by :

 

Volume of sphere - Volume of cylinder  =

 

(4/3)pi (radius of sphere)^3  -  pi * (radius of cylinder)^3 * cylinder height  =

 

pi  [     (4/3)* 5^3    -  (3)^2 * 8 ]   =

 

pi  [   500 / 3  - 72 ]  =

 

pi [ ( 500 - 216) / 3 ]  =

 

pi  [ 284 / 3 ]

 

So

 

W  =    284 / 3

 

 

cool cool cool

 Jan 2, 2019

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