Question

The altitude of a cone is 20 cm and its semi-vertical angle is \(30^\circ\). If the semi-vertical angle is increasing at the rate of \(2^\circ\) per second, then the radius of the base is increasing at the rate of:

• A. 30 cm/sec
• B. \(\frac{160}{3}\) cm/sec
• C. 10 cm/sec
• D. 160 cm/sec

Hint:

When dealing with rates of change of geometrical quantities, ensure that you use the correct trigonometric relations and convert angular velocity to radians if necessary.