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प्रश्न
A stone is dropped into a pond causing ripples in the form of concentric circles. The radius r of the outer ripple is increasing at a constant rate at 2 cm per second. When the radius is 5 cm find the rate of changing of the total area of the disturbed water?
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उत्तर
Radius = r
Rate of changes of radius `"dr"/"dt"` = 2
Given r = 5 cm
Area of circle A = πr2
Differentiating w.r.t ‘t’,
`"dA"/"dt" = 2pi"r" "dr"/"dt"`
= 2π (5) (2)
= 20 π
∴ Area of circle (ripple) is increasing at the rate of 20 π cm2/sec.
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