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 Find : 

(i) the total length of the silver wire required.

(ii) the area of each sector of the brooch.

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.

(i) The Total Length of Silver Wire Required

• Circumference of the circle: 2 × π × radius = π × diameter = π × 35 mm ≈ 109.96 mm (using π ≈ 3.14)
• Length of 5 diameters: 5 × 35 mm = 175 mm
• Total length of silver wire: Circumference + 5 diameters = 109.96 mm + 175 mm ≈ 284.96 mm

Note: The circumference calculation uses 2πr (with r = 17.5 mm), and adding 5 diameters gives the total wire length.

(ii) The Area of Each Sector of the Brooch

• Area of the circle: π × radius² = π × (17.5)² ≈ 962.11 mm²
• Area of each sector: Area of circle / 10 = 962.11 mm² / 10 ≈ 96.21 mm²