Question

A balloon which always remains spherical, is being inflated by pumping in $900$ cubic centimetres of gas per second. The rate at which the radius of the balloon is increasing when the radius is $15cm$ is.

• A. $\frac{1}{\pi }cm/sec$
• B. $\frac{2}{\pi }cm/sec$
• C. $\pi cm/sec$
• D. $\frac{\pi }{2}cm/sec$

Answer 1

The correct option is A $\frac{1}{\pi }cm/sec$

Given $\frac{dV}{dt}=900c{m}^3/sec$
Volume of sphere $V=\frac{4}{3}\pi r^3$
$\Rightarrow \frac{dV}{dt}=4\pi r^2\frac{dr}{dt}$
$\Rightarrow 900=4\times \pi \times 225\times \frac{dr}{dt}$
$\Rightarrow \frac{dr}{dt}=\frac{1}{\pi }cm/sec$