SOLUTION: A cube & a sphere have equal volumes. find the ratio of the radius of the sphere to an edge of the cube?

Algebra ->  Bodies-in-space -> SOLUTION: A cube & a sphere have equal volumes. find the ratio of the radius of the sphere to an edge of the cube?      Log On


   

Question 763128: A cube & a sphere have equal volumes. find the ratio of the radius of the sphere to an edge of the cube?
Answer by ramkikk66(644) About Me  (Show Source):
You can put this solution on YOUR website!
Let the radius of the cube be 'r' and edge of the cube be 'd'
Volume of cube = d^3
Volume of sphere = %284%2F3%29%2Api%2Ar%5E3 = 4.19%2Ar%5E3 (approx)
Given that both volumes are equal
d^3 = 4.19*r^3
r^3/d^3 = 1/4.19 = 0.2387
r/d = %280.2387%29%5E%281%2F3%29 = 0.6203 (approximately)

Ratio of radius of sphere to edge of cube = highlight%280.6203%29
:)