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Grade Upto college level Algebra

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.

Manvendra Singh chahar

12 Years agoGrade Upto college level

1 Answer

Jitender Singh

12 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

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