﻿CIRCULAR MEASURE

PAPER 1

1. Diagram 1 shows a sector ROS with centre O. Given that the length of the arc RS is 7.24 cm and the perimeter of sector ROS is 25 cm. Find the angle in radians.
[3 marks]

DIAGRAM 1

2. Diagram 2 shows a circle with centre O. Given that the length of the major arc AB is 45.51 cm, find the length , in cm , of the radius of the circle . [Use π = 3.142] [3 marks]

DIAGRAM 2

3. Diagram 3 shows a circle with centre O. The length of the major arc AB is 16 cm and the angle of the major sector AOB is 290º. [Use π = 3.142]
Find
(a) the value of in radians, correct to 3 decimal places ,
(b) the radius of the circle in cm. [3 marks]

DIAGRAM 3

(b)............................

4. Diagram 4 shows two sectors of two concentric circles, OAMB and OPQ , both with centre O . A is the midpoint of OP.

DIAGRAM 4
The length of the arc PQ is 13 cm and the length of OP is 10 cm. [Use = 3.142]
Find
(a) the value of , in radians , correct to four significant figures ,
(b) the area of the shaded sector . [3 marks]

(b)............................
5. Diagram 5 shows sector OAB with centre O and sector AXY with centre A.

DIAGRAM 5

Given that OB = 10 cm , AY = 4 cm , radians and the length of arc
AB = 7 cm , calculate
(a) the value of , in radian ,
(b) the area , in cm, of the shaded region . [4 marks]