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This problem trains for: SAT-I, AMC-8, GMAT, SAT-II.

A small sphere is inside a larger sphere. If the volume of the little sphere varies quadratically with the radius of the large sphere, by what factor does the volume of the large sphere increase if the radius of the small sphere increases

The volume of a sphere varies cubically with the radius of the sphere:

Denote the radius of the large sphere with RL.

Therefore, if the radius of the small sphere increases

The volume of the small sphere is:

and becomes:

The new volume of the large sphere: