Arc & Sector Formula

Arc & Sector Formula
GAM 2012 IB Preparation
1. The diagram below shows a circle centre O, with radius r. The length of arc ABC is 3 cm and =(a) Find the value of r.
(2)
(b) Find the perimeter of sector OABC.
(2)
(c) Find the area of sector OABC.
(2)(Total 6 marks)
2. The diagram below shows a circle of radius r and centre O. The angle = .

The length of the arc AB is 24 cm. The area of the sectorOAB is 180 cm2.
Find the value of r and of .
(Total 6 marks)



3. In the following diagram, O is the centre of the circleand (AT) is the tangent to the circle at T.
Diagram not to scale
If OA = 12 cm, and the circle has a radius of 6 cm, find the area of the shaded region.Working: | |
| Answer: ....................................................................... |
(Total 4 marks)4. The following diagram shows a circle of centre O, and radius 15 cm. The arc ACB subtends an angle of 2 radians at the centre O.

Find(a) the length of the arc ACB;
(b) the area of the shaded region.
(Total 6 marks)

5. The diagrams show a circular sector of radius 10cm and angle θ radians which is formed into a cone of slant height 10 cm. The vertical height h of the cone is equal to the radius r of its base. Find the angle θ radians.Working: | |
| Answer: ...................................................................... |...