The radius of a sphere is changing at the rate of 0.1 cm/sec. The rate of change of its surface area when the radius is 200 cm is

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KollegeApply · Accepted Answer

160$\pi$ cm2/sec \text { Let r be the radius and S be the surface area of the sphere at any time t.Then }, S = 4$\pi$ r^2 \RightarrowdS/dt=8$\pi$ rdr/dt \RightarrowdS/dt=8$\pi$\left( 200 \right)\left( 0 . 1 \right) \RightarrowdS/dt {=160$\pi$ \ cm}^2 /sec

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