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. 54π cm²/min

B. 7π cm²/min

C. 27 cm²/min

D. None of these

Answer 1

Correct answer is A.

The lateral surface area of a cone, with radius r and height h, is defined as

Given that r = 7cm, h = 24cm, \(\frac{dr}{dt}\) = 3cm/min and \(\frac{dh}{dt}\) = -4cm/min, we have to calculate \(\frac{dL}{dt}\)

Differentiating (1) with respect to t, we get

Substituting values, we get

Simplifying above equation, we get

\(\frac{dL}{dt}\) = 54π cm²/min