Question

The perimeter of the quadrant of a circle is 25 cm. Find its area. [CBSE 2012]

Answer 1

Let the radius of the circle be r
Now, Perimeter of quadrant = $\frac{1}{4}\left(2\mathrm{\pi }r\right)+2r$
$$\begin{gathered} \Rightarrow 25=\frac{1}{2}\times \frac{22}{7}\times r+2r \\ \Rightarrow 25=\frac{25r}{7} \\ \Rightarrow r=7\mathrm{cm} \end{gathered}$$
Area of quadrant = $\frac{1}{4}\mathrm{\pi }{r}^2=\frac{1}{4}\times \frac{22}{7}\times 7\times 7=38.5{\mathrm{cm}}^2$
Hence, the area of quadrant is 38.5 cm²