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Class 12
Mathematics
Application of Derivatives
the rate of change of the area of a circle with re...

Question:
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

Answer:

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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Question:
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

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Question: 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

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Question:
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