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

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KollegeApply · Accepted Answer

180$\pi$ 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 \RightarrowdV/dt=4$\pi$ r^2 dr/dt \RightarrowdV/dt=4$\pi$ \left( 15 \right)^2 $\times$ 0 . 2 \RightarrowdV/dt {=180$\pi$ \ cm}^3 /sec

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