Question

the radius of a sphere is halved. What fraction of the original volume is the volume of the smaller sphere

Answer 1

If the radius is halved (divided by 2, than the volume would be divided by 2 divided by 2 and divided by 2 again.

The reason is that the radius is only one dimensional (a line). Volume three dimensional, so the volume would be affected 3 times in the exact same way the one dimension is affected.

If 1 is divided by 2, divided by 2, and divided by 2 again, this is the same as saying

1/2 x 1/2 x 1/2

This equals 1/8.

The volume of the smaller sphere is 1/8 of the original.