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