Question

The perimeter of a circular field is 242 m. The area of the field is
(a) 9317 m²
(b) 18634 m²
(c) 4658.5 m²
(d) none of these

Answer 1

(c) 4658.5 m²
Let the radius be r m.
We know:
Perimeter of a circle$=2\mathrm{\pi }r$
Thus, we have:
$2\mathrm{\pi }r=242$
$$\begin{gathered} \Rightarrow 2\times \frac{22}{7}\times r=242 \\ \Rightarrow \frac{44}{7}\times r=242 \\ \Rightarrow r=\left(242\times \frac{7}{44}\right) \\ \Rightarrow r=\frac{77}{2} \end{gathered}$$

∴ Area of the circle$=\mathrm{\pi }{r}^2$
$$\begin{gathered} =\left(\frac{22}{7}\times \frac{77}{2}\times \frac{77}{2}\right){\text{m}}^2 \\ =4658.5{\text{m}}^2 \end{gathered}$$