Question

Gas is being pumped into a spherical balloon at the rate of $30f{t}^3$ $/min$. Then the rate at which the radius increase when it reaches the value $15ft$, is

• A. $\frac{1}{30\pi }$ ft/min
• B. $\frac{1}{15\pi }$ ft/min
• C. $\frac{1}{20}$ ft/min
• D. $\frac{1}{25}$ ft/min

Answer 1

The correct option is A $\frac{1}{30\pi }$ ft/min

Volume of sphere $V=\frac{4}{3}\pi r^3$

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

$\Rightarrow 30=4\pi \times 225\frac{dr}{dt}$

$\Rightarrow \frac{dr}{dt}=\frac{1}{30\pi }$ ft/min