Question

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.

Answer 1

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

Now, the rate of change of area (A) with respect to time (t) is given by,

It is given that,

∴

Thus, when r = 10 cm,

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