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

Total length of wire required will be the length of 5 diameters and the circumference of the brooch.

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

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

It can be observed from the figure that each of 10 sectors of the circle is subtending 36° at the centre of the circle.

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

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