Question

The area of a circular playground is $22176m^2$. Find the cost of fencing this ground at the rate of $Rs50permeter$.

Answer 1

Step 1- Finding the radius of the circle

Given,

Area of the circular playground $=22176m^2$

Cost of fencing $1$meter of ground $=Rs50$

Let us assume the radius of the circle to be $=r$

Area of the circle = $=\mathrm{\pi }{\mathrm{r}}^2$

$$\begin{gathered} \Rightarrow \mathrm{\pi }{\mathrm{r}}^2=22176 \\ \Rightarrow \left(\frac{22}{7}\right){\mathrm{r}}^2=22176 \\ \Rightarrow {\mathrm{r}}^2=22176\times \frac{7}{22} \\ \Rightarrow {\mathrm{r}}^2=1008\times 7 \\ \Rightarrow {\mathrm{r}}^2=7056 \\ \Rightarrow \mathrm{r}=\sqrt{7056} \\ \Rightarrow \mathrm{r}=84\mathrm{m} \end{gathered}$$

Hence, The radius of the circular playground $=84m$

Step 2 - Finding the cost of fencing

The circumference of the circle $=2\mathrm{\pi r}$

$$\begin{gathered} =2\times \left(\frac{22}{7}\right)\times 84 \\ =2\times 22\times 12 \\ =528m \end{gathered}$$

Cost of fencing $1$ meter of ground $=Rs50$

$\therefore$Cost of fencing the total ground$=Rs528\times 50$

$=Rs26400$

Hence, the Cost of fencing is $Rs26400$