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If a circular iron sheet of radius $30 \mathrm{~cm}$ is heated such that its area increases at the uniform rate of $6 \pi \mathrm{cm}^2 / \mathrm{hr}$, then the rate (in $\mathrm{mm} / \mathrm{hr}$ ) at which the radius of the circular sheet increases is
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The correct answer is:
$0.1$
$0.1$
Let $A=\pi r^2$.
$$
\begin{aligned}
\frac{d A}{d t} & =2 \pi r \cdot \frac{d r}{d t} \\
6 \pi & =2 \pi(30) \cdot \frac{d r}{d t} \\
\Rightarrow \quad \frac{3}{30}= & \frac{d r}{d t} \Rightarrow \frac{d r}{d t}=\frac{1}{10}=0.1
\end{aligned}
$$
Thus, the rate at which the radius of the circular sheet increases is $0.1$
$$
\begin{aligned}
\frac{d A}{d t} & =2 \pi r \cdot \frac{d r}{d t} \\
6 \pi & =2 \pi(30) \cdot \frac{d r}{d t} \\
\Rightarrow \quad \frac{3}{30}= & \frac{d r}{d t} \Rightarrow \frac{d r}{d t}=\frac{1}{10}=0.1
\end{aligned}
$$
Thus, the rate at which the radius of the circular sheet increases is $0.1$
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