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

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.