# The surface area of a spherical bubble is increasing at the rate of 2 cm2/sec. Find the rate at which the volume of the bubble is increasing at the instant if its radius is 6 cm.

Jitender Singh IIT Delhi
8 years ago
Ans:
Let radius of spherical bubble to be ‘r’.
Surface Area ‘S’:
$S = 4\pi r^{2}$
$\frac{\partial S}{\partial t} = 8\pi r.\frac{\partial r}{\partial t} = 2 \frac{cm^{2}}{sec}$
Volume ‘V’:
$V = \frac{4}{3}\pi r^{3}$
$\frac{\partial V}{\partial t} = 4\pi r^{2}. \frac{\partial r}{\partial t} =\frac{r}{2}.8\pi r.\frac{\partial r}{\partial t} = \frac{6}{2}.2 = 6\frac{cm^{3}}{sec}$
Thanks & Regards
Jitender Singh
IIT Delhi