Answer:
It can be concluded that reducing the radius to one-third will reduce the volume of sphere 1/27 times
Step-by-step explanation:
The volume of a sphere is given by the following formula:
[tex]V = \frac{4}{3}\pi r^3[/tex]
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: [tex]\frac{1}{3}r[/tex]
The new volume with the new radius will be:
[tex]V_1 = \frac{4}{3}\pi * (\frac{1}{3}r)^3\\V_1 = \frac{4}{3}\pi * \frac{1}{27}r^3\\V_1 = \frac{1}{27}(\frac{4}{3}\pi r^3)\\V_1 = \frac{1}{27}V[/tex]
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
