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 formula for the area of circle with radius r is,

A=π r 2

The change in area of the circle with respect to its radius is given by dA dr .

Differentiate with respect to r.

d( A ) dr = d( π r 2 ) dr dA dr =2πr (1)

(a)

Substitute r=3 cm in equation (1).

dA dr =2π( 3 ) =6π

Thus, the rate of change of area of the circle is 6π cm.

(b)

Substitute r=4 cm in equation (1).

d( A ) dr =2π( 4 ) =8π

Thus, the rate of change of area of the circle is 8π cm.