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:
(i) the total length of the silver wire required.
(ii) the area of each sector of the brooch.
Diameter (D) = 35 mm
Total number of diameters to be considered= 5
Now, the total length of 5 diameters that would be required = 35×5 = 175
Circumference of the circle = 2πr
Or, C = πD = 22/7×35 = 110
Area of the circle = πr2
Or, A = (22/7)×(35/2)2
= 1925/2 mm2
(i) Total length of silver wire required = Circumference of the circle + Length of 5 diameter
= 110 + 175 = 285 mm
(ii) Total Number of sectors in the brooch = 10
The area of each sector = total area of the circle/number of sectors
∴ Area of each sector = (1925/2) × 1/10
= 385/4 mm2