Question:
The area of a circular playground is $22176 \mathrm{~m}^{2}$. Find the cost of fencing this ground at the rate of $₹ 50$ per $\mathrm{m}$.
Solution:
Given, area of a circular playaround $=22176 \mathrm{~m}^{2}$
$\therefore \quad \pi r^{2}=22176 \quad\left[\because\right.$ area of circle $\left.=\pi r^{2}\right]$
$\Rightarrow$ $\frac{22}{7} r^{2}=22176 \Rightarrow r^{2}=1008 \times 7$
$\Rightarrow$ $r^{2}=7056 \Rightarrow r=84 \mathrm{~m}$
$\therefore$ Circumference of a circle $=2 \pi r=2 \times \frac{22}{7} \times 84$
$=44 \times 12=528 \mathrm{~m}$
$\therefore \quad$ Cost of fencing this ground $=528 \times 50=₹ 26400$
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