Question

If the radius of a sphere is reduced to one-third, by how many times does its
volume decrease?​

Answer 1

It can be concluded that reducing the radius to one-third will reduce the volume of sphere 1/27 times

Explanation:

The volume of a sphere is given by the following formula:

`V = (4)/(3)\pi r^3`

Here r is the radius of the sphere

Reducing the radius of sphere to one-third means dividing the radius by three. So the new radius will be:
`(1)/(3)r`

The new volume with the new radius will be:

`V_1 = (4)/(3)\pi * ((1)/(3)r)^3\\V_1 = (4)/(3)\pi * (1)/(27)r^3\\V_1 = (1)/(27)((4)/(3)\pi r^3)\\V_1 = (1)/(27)V`

The new volume is 1/27 times of the original volume.

Hence,

It can be concluded that reducing the radius to one-third will reduce the volume of sphere 1/27 times