Radius of a spherical balloon is increasing at the rate of 0.5 cm/sec; then the rate of increase of its volume when radius is 10 cm is

$200 \pi cm^3 / sec$

The correct answer is Option (2) → $200 \pi cm^3 / sec$

V, Volume of sphere = $\frac{4}{3}\pi R^3$

$\frac{dV}{dt}=\frac{4}{3}\pi 3R^2.\frac{dR}{dt}$

$=4\pi R^2×\frac{dR}{dt}=4\pi R^2×\frac{1}{2}=2\pi R^2$

$∴\left.\frac{dV}{dt}\right|_{R=10cm}=4\pi(10)^2×\frac{1}{2}=200 \pi cm^3 / \sec$