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

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 :
$$\eqalign{ & = \frac{4}{3}\pi {\left( {1.1R} \right)^3} \cr & = \frac{4}{3}\pi {R^3}\left( {1.331} \right) \cr} $$
Difference :
$$\eqalign{ & = \frac{4}{3}\pi {R^3}\left( {1.331} \right) - \frac{4}{3}\pi {R^3} \cr & = \frac{4}{3}\pi {R^3}\left( {1.331 - 1} \right) \cr & = \frac{4}{3}\pi {R^3}\left( {0.331} \right) \cr} $$
Increase % :
$$\eqalign{ & = \frac{{\frac{4}{3}\pi {R^3}\left( {0.331} \right)}}{{\frac{4}{3}\pi {R^3}}} \times 100 \cr & = 33.1\% \cr} $$