Question

The radius of the base of a cone is increasing at the rate of 3 cm/minute and the altitude is decreasing at the rate of 4 cm minute. The rate of change of lateral surface when the radius = 7 cm and altitude = 24 cm, is

• A. $54\pi \text{ cm}^2/\text{min}$
• B. $7\pi \text{ cm}^2/\text{min}$
• C. $27\pi \text{ cm}^2/\text{min}$
• D. None of these

Hint:

For related rates problems involving roots, it is often less prone to error if you define the intermediate variable (like slant height $l$) and evaluate its value first before plugging it into the differentiated formula.

Answer 1

The Correct Option is A