JEE Main2013MathematicsApplication of DerivativesActual

If the surface area of a sphere of radius r is increasing uniformly at the rate 8 ~cm ^2 / s , then the rate of change of its volume is:

Options

Aconstant
Bproportional to r
Cproportional to r^2
Dproportional to r

Correct answer

D. proportional to r

Step-by-step solution

aligned & V = 4 3 r^3 d ~V d t =4 r^2 d r d t & ~S =4 r^2 d ~S d t =8 r d r d t & 8=8 r d r d t d r d t = 1 r aligned Putting the value of d r d t in (i), we get d ~V d t =4 r^2 1 r =4 r d ~V d t is proportional to r .

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