Question

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

Answer 1

Answer:

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:

$V_{sphere} = \frac{4}{3}\pi R^{3}$

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:

$V'_{sphere} = \frac{4}{3}\pi R'^{3}$

$V'_{sphere} = \frac{4}{3}\pi (6R)^{3}$

$V'_{sphere} = 216\frac{4}{3}\pi R^{3}$

$V'_{sphere} = 216V_{sphere}$

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