Question

The radius of a sphere is increasing at the rate of 0.2 cm/sec. The rate at which the volume of the sphere increase when radius is 15 cm, is

विकल्प

• 12π cm³/sec

• 180π cm³/sec

• 225π cm³/sec

• 3π cm³/sec

Answer 1

180π cm³/sec

\[\text { Let r be the radius andVbe the volume of the sphere at any timet.Then },\]

\[V=\frac{4}{3}\pi r^3 \]

\[\Rightarrow\frac{dV}{dt}=4\pi r^2 \frac{dr}{dt}\]

\[\Rightarrow\frac{dV}{dt}=4\pi \left( 15 \right)^2 \times 0 . 2\]

\[\Rightarrow\frac{dV}{dt} {=180\pi \ cm}^3 /sec\]