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MHT CET202411 May 2024Morning 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

Options

  1. A0.1 ~cm ^3 / cm ^2
  2. B1 2 ~cm ^3 / cm ^2
  3. C1 ~cm ^3 / cm ^2
  4. D2 ~cm ^3 / cm ^2

Correct answer

C. 1 ~cm ^3 / cm ^2

Step-by-step solution

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

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