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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.

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.

Grade:12

1 Answers

Harshit Singh
askIITians Faculty 5963 Points
3 years ago
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

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