# 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 sector as shown in figure. Find : (i) The total length of the silver wire required. (ii) The area of each sector of the brooch.

(i) Length of silver wire used to make a brooch

$$= \ 2 \pi r$$, where $$r \ = \ \frac{35}{2}$$mm

$$= \ 2 \ × \ \frac{22}{7} \ × \ \frac{35}{2} \ = \ 110$$ mm

Wire used in 5 diameters $$= 5 \ × \ 35 \ = \ 175$$ mm

$$\therefore$$ Total wire used $$= (110 \ + \ 175) \ = \ 285$$ mm

(ii) The area of each sector of the brooch

$$= \ \frac{1}{10} \ ×$$ Area of the circle

$$= \ \frac{1}{10} \ × \ \pi r^2$$, where $$r \ = \ \frac{35}{2}$$mm

$$= \ \frac{1}{10} \ × \ \frac{22}{7} \ × \ ( \frac{35}{2} )^2 \ = \ \frac{385}{4}$$ mm2