Question

A cube and a sphere have equal volume. Find the ratio of the measure of an edge of the
cube to the radius of the sphere.
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Answer 1

Answer:

volume of cube is x 3

volume of sphere is 4/3πr3

Answer 2

Answer:

Vcube = s3 where s is the side length

Vsphere = (4/3)·pi·r3 where r is the sphere's radius

Since the volumes are stated to be equal, set them equal:

Vcube = Vsphere

s3 = (4/3)·pi·r3

3/4pi = r3/s3

3√(3/4pi) = r/s