If a sector of a circle has an area of 40 sq. units and a central angle of $72^{\circ}$, the radius of the circle is :
[1]
A piece of wire 20 cm long is bent into the form of an arc of a circle of radius $\frac{60}{\pi}\text{ cm}$. The angle subtended by the arc at the centre of the circle is :
[1]
A brooch is a decorative piece often worn on clothing like jackets, blouses or dresses to add elegance. Made from precious metals and decorated with gemstones, brooches come in many shapes and designs.
One such 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 the figure.
Based on the above given information, answer the following questions:
| (i) | Find the central angle of each sector. |
| (ii) | Find the length of the arc ACB. |
| (iii) | (a) Find the area of each sector of the brooch. |
| OR | |
| (iii) | (b) Find the total length of the silver wire used. |
[4]
An arc of a circle of radius 21 cm subtends an angle of $60^{\circ}$ at the centre. Find :
(i) the length of the arc.
(ii) the area of the minor segment of the circle made by the corresponding chord.
[5 marks]
A chord of a circle of radius 14 cm subtends an angle of \( 60^{\circ} \) at the centre. Find the area of the corresponding minor segment of the circle. Also find the area of the major segment of the circle.
[5 marks]
