Question

If the radius of a solid object increases 6 times, the volume of the object will increase how many times?

Answer 1

The volume will increase by 216 time of the original volume

Solution:

A sphere is a solid object.

Now, the volume of sphere is given by:

`V_(sphere) = (4)/(3)\pi R^(3)`

where

R = radius of the sphere

In the question the radius is increased 6 times, therefore, the new radius is:

R' = 6R

From the formula for the volume of sphere:

The volume of the sphere now becomes:

`V'_(sphere) = (4)/(3)\pi R'^(3)`

`V'_(sphere) = (4)/(3)\pi (6R)^(3)`

`V'_(sphere) = 216(4)/(3)\pi R^(3)`

`V'_(sphere) = 216V_(sphere)`

Thus the new volume will become 216 times of the original volume