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Question 1

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}

  1. 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.

  1. 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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