Question

The altitude of a cone is 20 cm and its semi-vertical angle is 30°. If the semi-vertical angle is increasing at the rate of 2° per second, then the radius of the base in increasing at the rate of

A. 30 cm/sec

B. \(\frac{160}{3}\) cm/sec

C. 10 cm/sec

D. 160 cm/sec

Answer 1

Correct answer is B.

The relation between height h, radius r and semi-vertical angle α is defined by

tan α = \(\frac{r}{h}\)

Given that h = 20cm

 tan α = \(\frac{r}{20}-(1)\)

Given that α = 30° and \(\frac{dα}{dt}\) = 2°/sec, we have to find \(\frac{dr}{dt}\)

Differentiating (1) with respect to t, we get

Substituting values, we get