Question

A spherical balloon is pumped at the rate of $2$ inch${}^3$/min, the rate of increase of its radius when its radius is $15$ inch is :

• A. $\frac{1}{30\pi }$inch / min
• B. $\frac{1}{60\pi }$inch / min
• C. $\frac{1}{90\pi }$inch / min
• D. $\frac{1}{450\pi }$inch / min

Answer 1

The correct option is D $\frac{1}{450\pi }$inch / min

Rate of increase in volume $=\frac{d}{dt}\left(\frac{4}{3}\pi r^3\right)=2$ .. (given)

$\Rightarrow 2=\frac{4\pi }{3}\times 3r^2\times \frac{dr}{dt}$

$\Rightarrow \frac{dr}{dt}=\frac{2}{4\pi r^2}=\frac{1}{2\pi \times {15}^2}$

$=\frac{1}{450\pi }$