If the radius of a sphere is increased by 10%, then the volume will be increased by :

Answer: Option A

If R is the radius of sphere, volume of the sphere = $$\frac{4}{3}\pi R^3$$
When radius of sphere is increased by 10%
New volume :
$$\begin{array}{rl}& =\frac{4}{3}\pi {\left(1.1R\right)}^3\\ & =\frac{4}{3}\pi R^3\left(1.331\right)\end{array}$$
Difference :
$$\begin{array}{rl}& =\frac{4}{3}\pi R^3\left(1.331\right)-\frac{4}{3}\pi R^3\\ & =\frac{4}{3}\pi R^3\left(1.331-1\right)\\ & =\frac{4}{3}\pi R^3\left(0.331\right)\end{array}$$
Increase % :
$$\begin{array}{rl}& =\frac{\frac{4}{3}\pi R^3\left(0.331\right)}{\frac{4}{3}\pi R^3}\times 100\\ & =33.1\%\end{array}$$