The radius of a circle is increasing at the rate

Question:

The radius of a circle is increasing at the rate of $0.7 \mathrm{~cm} / \mathrm{sec}$. What is the rate of increase of its circumference?

Solution:

Let $r$ be the radius and $C$ be the circumference of the circle at any time $t$. Then,

$C=2 \pi r$

$\Rightarrow \frac{d C}{d t}=2 \pi \frac{d r}{d t}$

$\Rightarrow \frac{d C}{d t}=2 \pi \times 0.7$          $\left[\because \frac{d r}{d t}=0.7 \mathrm{~cm} / \mathrm{sec}\right]$

$\Rightarrow \frac{d C}{d t}=1.4 \pi \mathrm{cm} / \mathrm{sec}$

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