Question

The radius of a sphere is changing at the rate of 0.1 cm/sec. The rate of change of its surface area when the radius is 200 cm, is

• A. 8π cm²/sec
• B. 12π cm²/sec
• C. 160π cm²/sec
• D. 200π cm²/sec

Answer 1

The correct option is C

160π cm²/sec

Let r be the radus and S be the surface area of the sphere at any time t. Then,
$S=4\pi r^2$
$\Rightarrow \frac{dS}{dt}=8\pi r\frac{dr}{dt}\Rightarrow {\left(\frac{dS}{dt}\right)}_{r-200}=8\pi \times 200\times 0.1=160\pi c{m}^2/sec$