Question

A brooch is made with silver wire in the form of a circle with diameter 35 mm. The wire is also used in making 5 diameters which divide the circle into 10 equal sectors as shown in Fig. 11.9. Find : 
(i) the total length of the silver wire required.
(ii) the area of each sector of the brooch.

Answer 1

The total wire length required is the sum of 5 diameters and the brooch's circumference.

Radius of the circle = \( \frac{35}{2} \) mm
Circumference of the brooch = \( 2πr \)
= \( 2 \times \frac{22}{7} \times (\frac{35}{2}) \) = 110 mm

Length of wire required = 110 + 5 × 35 = 110 + 175 = 285 mm

As depicted in the figure, 10 sectors of the circle each subtend an angle of 36° at the center.

Therefore, the area of each sector = \( \frac{36°}{360°} \times \pi r^2 \)

= \( \frac{1}{10} \times \frac{22}{7} \times (\frac{35}{2}) \times (\frac{35}{2}) \) = \( \frac{385}{4} \, mm^2 \)