Question

the radius r cm of a lot of ink is increasing at the rate of 0.15 mm per second .find the rate at which the area A is increasing when the radius is 600
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Answer 1

Correct Question :-

The radius r of a blot of ink is increasing at the rate of 0.15 mm per second. Find the rate at which the area is increasing when the radius is 600 mm.

Given :-

◉ Rate of increasing of radius, dr/dt = 0.15 mm

To Find :-

◉ Rate at which area is increasing when the radius is 600 mm.

Solution :-

⇒ Area = πr²

⇒ A = πr²

Differentiate both sides w.r.t t

⇒ dA/dt = π • d(r²)/dt

⇒ dA/dt = π • [ d(r²) / dr × dr/dt ]

⇒ dA/dt = π • [ 2r × dr/dt ]

⇒ dA/dt = 2πr × 0.15 [ given ]

⇒ dA/dt = 0.3πr

Given, Radius, r = 600 mm

∴ dA/dt = 0.3 × π × 600

⇒ dA/dt = 180π mm²

Hence, The area would increase at the rate of 180π mm².