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A sphere and a cube have same surface area. Find the ratio of volume of sphere to that of cube.

 Jan 13, 2020
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The  surface area of the cube  =  6s^2   (1)     where s is the side of the cube

 

And the  volume of the  cube = s^3

 

The surface area of the  sphere  =  4pi r^2    (2)   where r  is the radius of the sphere

 

Equating (1)  and (2) we have that

 

6s^2  = 4pi r^2          divide both sides by  4pi

 

6 s^2 / [ 4 pi ] =  r^2

 

[ 3 s^2 / (2 pi) ]  = r^2          take the positive root of both sides

 

r = s √ [3 / (2pi )  ]

 

So   the

 

Volume of Sphere              (4/3) pi r^3           (4/3) pi  [  s √ [3 / (2pi )  ]^3

_______________  =       __________  =    _______________________   =

Volume of Cube                    s^3                                s^3

 

 

(4/3)pi (3/ (2pi))^(3/2)  =

 

(4/3)pi * √ [ 3 /( 2pi) ]^3

 

 

cool cool cool

 Jan 13, 2020

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