A circular disc of radius 3 cm is being heated. Due to expansion, its radius increases at the rate of 0.05 cm/sec. Find the rate at which its area is increasing when the radius is 3.2 cm.

Question

Philoid · Accepted Answer

Let r be the radius of the circular disc and A be the area of the circular disc at any instant of time.

We know that, the area of the circle

Differentiating both sides with respect to t, we get

As per the given criteria, the circular disc expands on heating with the rate of change of radius is 0.05cm/s, i.e.,

Substituting this value in equation (i), we get

When the radius is 3.2 cm, the above equation becomes

So the rate at which its area is increasing when radius is 3.2 cm is 0.32 cm²/sec