Question

A balloon which always remains spherical is being inflated by pumping in 10 cubic centimeters of gas per second. Find the rate at which the radius of the balloon is increasing when the radius in 15 cms.

• A. $\frac{1}{90\pi }cm/sec$
• B. $\frac{1}{9\pi }cm/sec$
• C. $\frac{1}{30\pi }cm/sec$
• D. $\frac{1}{\pi }cm/sec$

Answer 1

The correct option is A

$\frac{1}{90\pi }cm/sec$

$v=\frac{4}{3}\pi r^3$
$\frac{dv}{dt}=4\pi r^2\frac{dr}{dt}\Rightarrow \frac{dr}{dt}=\frac{1}{90\pi }$