Question

Find the rate of change of the area of a circle with respect to its radius r when

(a) r = 3 cm  (b) r = 4 cm

Answer 1

The area of a circle (A) with radius (r) is given by,

A= πr²

Now, the rate of change of the area with respect to its radius is given by,

Hence, the area of the circle is changing at the rate of 6π cm²/s when its radius is 3 cm.
2. When r = 4 cm,

Hence, the area of the circle is changing at the rate of 8π cm²/s when its radius is 4 cm.