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The radius of a sphere is increasing at a rate \(3cm s^{-1}\...

The radius of a sphere is increasing at a rate 3cms1. Find the rate of increase in the surface area, when the radius is 2cm. 

A.

8πcm2s1

B.

16πcm2s1

C.

24πcm2s1

D.

48πcm2s1

Correct answer is D

Surface area of sphere, A=4πr2

dAdr=8πr

The rate of change of radius with time drdt=3cms1

dAdt=(dAdr)(drdt)

= 8π×2cm×3cms1=48πcm2s1