Question

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

Answer 1

When the radius of a sphere is halved, the volume of the smaller sphere is one-eighth of the original volume.

Step-by-step explanation:

When the radius of a sphere is halved, the volume of the smaller sphere is one-eighth of the original volume. This is because the volume of a sphere is directly proportional to the cube of its radius. So, if the radius is halved, the volume will decrease by a factor of (1/2)^3, which is 1/8.

For example, if the original volume of the sphere is V, the volume of the smaller sphere would be 1/8V.

Answer 2

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.