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

 Mar 27, 2018
 #1
avatar+103123 
+1

Call the radius  of the cylinder and sphere, r

And the height  of the cylinder  = 2r

 

So

 

60  =  pi * r^2 * 2r

30 =  pi * r^3

30/pi  =  r^3

[30/pi]^1/3  =  r

 

So...the volume of the sphere is

 

(4/3)pi [ (30/pi)^1/3 ]^3  =

(4/3) pi * 30/pi  =

40 cm^3

 

We could  also  see this by the forllowing ratio

 

Vsphere      =   (4/3)pi *r^3              (4/3)                4                 2            40

_______          __________    =      _____  =     ______  =      __    =    ___

V cylinder         pi * r^2 * 2r                2                  6                  3            60

 

 

cool cool cool

 Mar 27, 2018
 #2
avatar+4322 
0

Thanks so much, CPhill!!!!!

tertre  Mar 27, 2018

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