MHT CET202410 May 2024Evening ShiftMathematicsApplication of DerivativesActual

The volume of a ball is increasing at the rate of 4 cc / sec . The rate of increase of the radius, when the volume is 288 cc , is

Options

A1 6 ~cm / sec
B1 36 ~cm / sec
C6 ~cm / sec
D36 ~cm / sec

Correct answer

B. 1 36 ~cm / sec

Step-by-step solution

aligned & V= 4 3 r^3 & 288 = 4 3 r^3 & r=6 ~cm aligned aligned & V = 4 3 r ^3 & dV dt =4 r ^2 dr dt & 4 =4 r ^2 dr dt & dr dt = 1 r ^2 = 1 36 ~cm / sec aligned

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