3) 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.

Answers (1)

Radius of a circle is increasing uniformly at the rate \left ( \frac{dr}{dt} \right ) =  3 cm/s 
Area of circle(A) = \pi r^{2}
\frac{dA}{dt} =\frac{dA}{dr}.\frac{dr}{dt}                            (by chain rule)
\frac{dA}{dt} =\frac{d \pi r^{2}}{dr}.\frac{dr}{dt} = 2\pi r \times 3 = 6\pi r
It is given that the value of r = 10 cm
So,
       \frac{dA}{dt} = 6\pi \times 10 = 60\pi \ cm^{2}/s
Hence,  the rate at which the area of the circle is increasing when the radius is 10 cm  is  60\pi \ cm^{2}/s

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