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.

Let us given that, 

Diameter of the brooch = D = 35 mm

Thus, Radius of the brooch = D/2

= 35/2 mm

(i) The total length of the silver wire required:

total length of the silver wire required = Circumference of brooch $+$ (5 $\times$ D)

= $\mathrm{\pi }$D $+$ 5D

= D ($\mathrm{\pi }$  $+$ 5)

= 35 $\times$ ( 22/7 $+$ 5)

= 57 $\times$ 5

= 285 mm

(ii) The area of each sector of the brooch: 

Radius of the brooch = D/2 = 35/2 mm

here, the wire divides the brooch into 10 equal parts

Hence, The angle of sector = $\theta$ = 360⁰/10 = 36⁰

Thus, The area of each sector of the brooch =  $\frac{{36}^0}{{360}^0}$ $\times$ $\mathrm{\pi }$ r²

by putting the values of $\mathrm{\pi }$ and r we get, 

 The area of each sector of the brooch = 96.25 mm²