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The volume of a cylinder is 60 cubic centimeters. The radius of the cylinder is 2. What is the number of cubic centimeters in the volume of the sphere that circumscribes the cylinder?

 Apr 22, 2022
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We can find the height of the  cylinder as follows

 

60 =   pi * 2^2  * height

 

15 / pi  =  height

 

Now.....the radius  of  the sphere  can  be found by the Pythagorean Theorem

 

We have a right triangle with one leg  =  the radius of the cylinder = 2  and the other  =  (1/2) the height of the cylinder =  7.5 / pi

 

The radius of the sphere is  the hypotenuse of this  triangle   = sqrt  [ 2^2 + (7.5/pi)^2  ]  = 

 

sqrt  [ 4 + 56.25/pi^2 ]  =   [ 4 + 56.25 / pi^2]^(1/2)  

 

The   volume of this  sphere  =    (4/3) pi * [  4 + 56.25/pi^2] ^(3/2)  ≈  126.5  cm^3

 

 

cool cool cool

 Apr 22, 2022

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