Question

A brooch is made with silver wire in the form of a circle with a diameter $35mm$. The wire is also used in making $5$ diameters which divide the circle into $10$ equal sectors as shown in the figure. Find :
(i) The total length of the silver wire required.
(ii) The area of each sector of the brooch.

Answer 1

The diameter of circle is $35mm$

The circumference $=2\pi r$
$=2\times \frac{22}{7}\times 35=220mm$

The length of $5$ diamters $=5\times 35=175mm$

(i) Total wire needed $=220mm+175mm=395mm$

Hence, total length of silver wire required is $395mm$.

(ii) The circle is divided into $10$ equal parts,
so the angle of sector is $\frac{{360}^{\circ }}{10}={36}^{\circ }$

The area of sector $=\frac{\text{central angle}}{{360}^{\circ }}\times \pi r^2$
$=\frac{{36}^{\circ }}{360}\times \pi r^2=\frac{1}{10}\times 227\times 35\times 35=385c{m}^2$

Hence, the area of each sector of brooch is $385c{m}^2$.