A sphere and a cube have same surface area. Find the ratio of volume of sphere to that of cube.
+128470 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
