Question

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

• A. $8\pi c{m}^2/sec$
• B. $12\pi c{m}^2/sec$
• C. $160\pi c{m}^2/sec$
• D. $200\pi c{m}^2/sec$

Answer 1

Answer: (C)

$160\pi c{m}^2/sec$

$S=4\pi r^2$

$\frac{dS}{dt}=8\pi r.\frac{dr}{dt}$

$\frac{dS}{dt}=8\pi \left(200cm\right).\left(0.1\right)cm/sec$

$=160\pi c{m}^2/sec$