If a metallic circular plate of radius 50 cm is heated so that its radius increases at the rate of 1 mm per hour, then the rate at which, the area of the plate increases (in cm 2 / hour) is

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Let A = π r 2 be area of metalic circular plate of r = 50 cm . Also, given d t d r ​ = 1 mm = 10 1 ​ cm ​ ∴ A = π r 2 ⇒ d t d A ​ = 2 π r d t d r ​ = 2 π ⋅ 50 ⋅ 10 1 ​ = 10 π ​ Hence, area of plate increases in 10 π cm 2 / hour.

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