A circular disc of radius 3 cm is being heated. Due to expansion, its radius increases at a rate of 0.05 cm per second. Find the rate at which its area is increasing if the radius is 3.2 cm.

Dear Student

Let us assume that “r” be the radius of the given disc and “A” be the area, then the area is given as:

A = πr^2

By using the chain rule,

Then dA/dt = 2πr(dr/dt)

Thus, the approximate rate of increase of radius = dr = (dr/dt) ∆t = 0.05 cm per second

Hence, the approximate rate of increase in area is:

dA = (dA/dt)(∆t) = 2πr[(dr/dt) ∆t ]

= 2π (3.2) (0.05)

= 0.320π cm^2per second.

Therefore, when r= 3.2 cm, then the area is increasing at a rate of 0.320π cm^2/second.

Thanks