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MHT CET202416 May 2024Evening ShiftMathematicsApplication of DerivativesActual

The rate of change of the volume of a sphere with respect to its surface area, when its radius is 2 cm, is _______ cm ^3 / cm ^2 .

Options

  1. A0.1
  2. B0.5
  3. C1
  4. D2

Correct answer

C. 1

Step-by-step solution

Volume of sphere (V)= 4 3 r^3 Surface area of sphere (A)=4 r^2 aligned & d V d r =4 r^2 and d A d r =8 r & d V d A = d V d r d A d r d r = 4 r^2 8 r = r 2 & ( d V d A )_ r=2 = 2 2 =1 ~cm ^3 / cm ^2 aligned

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