If the radius of a sphere is increased by 4 cm, its surface area is increased by 464π cm². What is the volume (in cm³) of the original sphere?

Solution (By Examveda Team)

$$\eqalign{ & 4\pi \left[ {{{\left( {R + 4} \right)}^2} - {R^2}} \right] = 464\pi \cr & 4\left( {R + 4 + R} \right)\left( {R + 4 - R} \right) = 464 \cr & 16\left( {2R + 4} \right) = 464 \cr & 2R + 4 = 29 \cr & R = \frac{{25}}{2} \cr & {\text{Volume of sphare}} = \frac{4}{3}\pi {R^3} \cr & = \frac{4}{3}\pi \times {\left( {\frac{{25}}{2}} \right)^3} \cr & = \frac{4}{3} \times \frac{{15625}}{8}\pi \cr & = \frac{{15625}}{6}\pi \cr} $$