The radius of a circle is increasing uniformly at the rate of 3 cm/s. Find the rate at which the area of the circle is increasing when the radius is 10 cm.

Question

Philoid · Accepted Answer

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

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

It is given that

Then,

Thus, when r = 10cm

Then

Therefore, the rate at which the area of the circle is increasing when the radius is 10 cm is 60π cm²/s.