17) The rate of change of the area of a circle with respect to its radius r at r = 6 cm is
(A) 10π      (B) 12π       (C) 8π          (D) 11π

Answers (1)

Area of circle(A) = \pi r^{2}
\frac{dA}{dr} = \frac{d(\pi r^{2})}{dr} = 2\pi r
Now, at r = 6cm
\frac{dA}{dr}= 2\pi \times 6 = 12\pi cm^{2}/s
Hence, the rate of change of the area of a circle with respect to its radius r at r = 6 cm is 12\pi cm^{2}/s
Hence, the correct answer is B

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