If you doubled the radius of a sphere, how would the volume change?

A.
The volume would double.
B.
The volume would triple.
C.
The volume would quadruple.
D.
The volume would increase to be eight times that of the original volume.

Question

If you doubled the radius of a sphere, how would the volume change?

A.
The volume would double.
B.
The volume would triple.
C.
The volume would quadruple.
D.
The volume would increase to be eight times that of the original volume.

phi · Answer

there are (at least) two ways to figure this out.
one way is write down the formula for the volume of a sphere,  and put in 2r in place of r
the other way is to know that if you multiply a "side length" by k, then the surface area increases by k^2  and the volume of a 3D figure increases  by k^3