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Question
The radius of a sphere is increasing at the rate of 0.2 cm/sec. The rate at which the volume of the sphere increase when radius is 15 cm, is
Options
12π cm3/sec
180π cm3/sec
225π cm3/sec
3π cm3/sec
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Solution
180π cm3/sec
\[\text { Let r be the radius andVbe the volume of the sphere at any timet.Then },\]
\[V=\frac{4}{3}\pi r^3 \]
\[\Rightarrow\frac{dV}{dt}=4\pi r^2 \frac{dr}{dt}\]
\[\Rightarrow\frac{dV}{dt}=4\pi \left( 15 \right)^2 \times 0 . 2\]
\[\Rightarrow\frac{dV}{dt} {=180\pi \ cm}^3 /sec\]
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