Question

A spherical balloon is pumped at the rate of $10inc{h}^3$ /min, the rate of increase of its radius if 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. $\frac{1}{120\pi }inch/min$

Answer 1

The correct option is C $\frac{1}{90\pi }inch/min$

Let V be the volume and r the radius of the balloon at any time t.
$\therefore V=\frac{4}{3}\pi r^3\therefore \frac{dv}{dt}=\frac{4}{3}\pi \left(3r^2\right)\frac{dr}{dt}\Rightarrow 10=\frac{4\pi }{3}.3.(15{)}^2\frac{dr}{dt}\therefore \frac{dr}{dt}=\frac{1}{90\pi }inch/min$