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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.

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3 months ago Anand Kumar Pandey
3121 Points
```							Dear StudentLet us assume that “r” be the radius of the given disc and “A” be the area, then the area is given as:A = πr^2By 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 secondHence, 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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3 months ago
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