Question

The rate of change of volume of a sphere with respect to its diameter, when its radius is 5 cm, is :

• A. \( 400\pi \text{ cm}^3/\text{cm} \)
• B. \( 100\pi \text{ cm}^3/\text{cm} \)
• C. \( 50\pi \text{ cm}^3/\text{cm} \)
• D. \( 25\pi \text{ cm}^3/\text{cm} \)

Hint:

Always note carefully the variable with respect to which the rate of change is asked. Differentiating with respect to diameter (\(D\)) is different from differentiating with respect to radius (\(r\)). Always use the chain rule relation: \( \frac{dV}{dD} = \frac{1}{2}\frac{dV}{dr} \).

Answer 1

The Correct Option is D