SOLUTION: If a ball and a cube have the same volume, what is the ratio between the surface areas of the ball and the cube?

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Question 287582: If a ball and a cube have the same volume, what is the ratio between the surface areas of the ball and the cube?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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If a ball and a cube have the same volume, what is the ratio between the surface
areas of the ball and the cube?
:
Choose a convenient value for the volume; 1000
then
side of cube = 10
S.A. = 6(10^2)
SA = 600 Sq/units; cube
:
Find the radius
%284%2F3%29pi%2Ar%5E3 = 1000
multiply both sides by 3:
4pi%2Ar%5E3 = 3(1000)
r^3 = 3000%2F%284%2Api%29
r = 238.732%5E%281%2F3%29
r = 6.2
Find the surface area
SA = 4%2Api%2A6.2%5E2
SA = 483.6 sq/units; sphere
:
Sphere/cube S.A. ratio: 483.6%2F600 ~ 4%2F5