Question

If the volume of a spherical balloon is increasing at the rate of 900 cm²/sec. then the rate of change of radius of balloon at instant when radius is 15 cm [in cm/sec]

• A. $\frac{22}{7}$
• B. 22
• C. $\frac{7}{22}$
• D. None of these

Answer 1

Answer: (C)

$\frac{7}{22}$

Answer 2

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

Differentiate with respect to t

$\frac{dV}{dt} = \frac{4}{3}\pi 3r^{2}.\frac{dr}{dt}$ ⇒ $\frac{dr}{dt}$ ⇒ $\frac{1}{4\pi r^{2}}.\frac{dV}{dt}$

$\frac{dr}{dt} = \frac{1}{4 \times \pi \times 15 \times 15} \times 900$ $= \frac{1}{\pi} = \frac{7}{22}$.