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

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

Philoid · Accepted Answer

(a) We know that area of a circle (A) is A = πr²

Then, Rate of change of the area with respect to its radius is given by,

When r = 3cm

Then

Therefore, the area of the circle is changing at the rate of 6πcm²/s when its radius is 3cm.

(b) We know that area of a circle (A) is A = πr²

Then, Rate of change of the area with respect to its radius is given by,

When r = 4cm

Then

Therefore, the area of the circle is changing at the rate of 8πcm²/s when its radius is 4cm.