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  • The area of a circle of radius r increases at the rate of a 5cm square /sec;Find the rate at which the radius increases.

The area of a circle of radius r increases at the rate of a 5cm square /sec;Find the rate at which the radius increases.

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Let r cm be the radius and A be the area enclosed by it at any time t seconds,then A=pi r^2......(i)
Differentiating (i) w.r.t. t,we get
fracmathrmd Amathrmd t=pi .2rfracmathrmd rmathrmd t=2pi rfracmathrmd rmathrmd t , ,: : : : : : : butfracmathrmd amathrmd t=5cm^2/sec, (given)
Rightarrow 5=2pi rfracmathrmd rmathrmd tRightarrow fracmathrmd rmathrmd t=frac52pi r
Hence,the radius is increasing at the rate of frac52pi r, , cm/sec.

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Deependra Verma

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