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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.

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.

Grade:Upto college level

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
9 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
askIITians Faculty

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