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Question
The radius of a circle is increasing uniformly at the rate of 3 cm/s. Find the rate at which the area of the circle is increasing when the radius is 10 cm.
Solution
Let the radius of the cube = r
Given `(dr)/dt = 3 cm//s`
Rate of change of A with respect to t, `(dA)/dt`
`= 2pi r (dr)/dt`
`= 2pi r (3) = 6 pi r`
r = 10 cm
`therefore (dA)/dt = 6 pi` (10) = 60`pi` cm2/s
=> Rate of increase of area of the circle 60`pi` cm2/sec.
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