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Class 12
Mathematics
Application of Derivatives
find the rate of change of the area of a circle wi...

Question: Find the rate of change of the area of a circle with respect to its radius r when
(a) r = 3 cm
(b) r = 4 cm

Answer:

The area of a circle (A) with radius (r) is given by,

A = πr²

Now, the rate of change of the area with respect to its radius is given by,

\begin{align} \frac{dA}{dr} = \frac{d}{dr}(πr^2) = 2πr \end{align}

When r = 3 cm,

\begin{align} \frac{dA}{dr} = 2π (3) = 6π \end{align}

Hence, the area of the circle is changing at the rate of 6π cm²/s when its radius is 3 cm.

When r = 4 cm,

\begin{align} \frac{dA}{dr} = 2π (4) = 8π \end{align}

Hence, the area of the circle is changing at the rate of 8π cm²/s when its radius is 4 cm.

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Question: Find the rate of change of the area of a circle with respect to its radius r when
(a) r = 3 cm
(b) r = 4 cm

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Question: Find the rate of change of the area of a circle with respect to its radius r when (a) r = 3 cm (b) r = 4 cm

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Question: Find the rate of change of the area of a circle with respect to its radius r when
(a) r = 3 cm
(b) r = 4 cm