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 figure. Find.

1. The total length of the silver wire required.
2. The area of each sector of the brooch [Use π = `22/7`]

Answer 1

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

Radius of circle = `35/2` mm

Circumference of brooch = 2πr

`= 2 xx 22/7xx (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 = `36^@/360^@ xx pir^2`

`=1/10xx22/7xx(35/2)xx(35/2)`

= `385/4` mm²