Question

If radius of a sphere is doubled what percentage increase the volume

Answer 1

The original case: V=(43)⋅π⋅r3

Now you have 2r (instead of r)

The new situation: V'=(43)⋅π?(2r)3

Since the first two terms are identical you can cancel them:

V'V=(2r)3r3

which will yield:

V'V=8r3r3

Finally you will have V'V=8

In other words, in the new case you will have 8 times larger volume.