Class 12 Mathematics - Chapter Application of Derivatives NCERT Solutions | The rate of change of the area of a circ
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
The area of a circle (A) with radius (r) is given by,
A = πr2
Therefore, the rate of change of the area with respect to its radius r is
\begin{align}\frac{dA}{dr} = \frac{d}{dr}(\pi r^2) = 2\pi r\end{align}
∴When r = 6 cm,
\begin{align}\frac{dA}{dr} = 2\pi \times 6 =12 \pi\; cm^2/s\end{align}
Hence, the required rate of change of the area of a circle is 12π cm2/s.
The correct answer is B.
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How the units of rate of change of area with respect for cm2 /sec
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