A stone is dropped into a quiet lake and waves in the form of circles are generated. Radius of the circular wave increases at the rate of 3 cm/sec. How fast the area enclosed is increasing when the radius is 8 cm?

Q.12 A stone is dropped into a quiet lake and waves in the form of circles are generated. Radius of the circular wave increases at the rate of 3 cm/sec. How fast the area enclosed is increasing when the radius is 8 cm?

Doubtly Asked 28 Oct 2026 Board exam · March 2026 hsc 12th Save WhatsApp Report

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Answer: \(48\pi\) cm\(^2\)/sec

Area \(A = \pi r^2\), so \(\dfrac{dA}{dt} = 2\pi r\dfrac{dr}{dt}\).

With \(r = 8\) cm and \(\dfrac{dr}{dt} = 3\) cm/sec: \(\dfrac{dA}{dt} = 2\pi(8)(3) = 48\pi\) cm\(^2\)/sec.

Doubtly AI · 28 Oct 2026 AI-verified · Oct 2026 Report

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A stone is dropped into a quiet lake and waves in the form of circles are generated. Radius of the circular wave increases at the rate of 3 cm/sec. How fast the area enclosed is increasing when the radius is 8 cm?

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