Question

If the radius of a sphere is doubled, then its volume is increased by what per cent?

Answer 1

We have a sphere of radius '$r$'.

Volume of the sphere will be $=\frac{4}{3}\pi r^3$

Now, when radius is doubled we have $2r$

Volume will be $=\frac{4}{3}\pi (2r{)}^3=\frac{4}{3}\pi 8r^3$

$\%$ increase $=\frac{\text{Increased volume - Original volume}}{\text{Original volume}}$

$\%$ increase $=\frac{\frac{4}{3}\pi 8r^3-\frac{4}{3}\pi r^3}{\frac{4}{3}\pi r^3}$

$\%$ increase $=\frac{\frac{4}{3}\pi r^3(8-1)}{\frac{4}{3}\pi r^3}\times 100=700\%$