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# 2 circular measure arc length

## on Sep 03, 2011

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This presentation shows how to find the arc length and area of sector of a circle

This presentation shows how to find the arc length and area of sector of a circle

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## 2 circular measure arc lengthPresentation Transcript

• Circular Measure
Arc Length and Area of a Sector
In general, if the length of arc, s units and the radius is r units, then
That is the size of the angle (θ) is given by
the ratio of the arc length to the length of the radius.
For example:
If s = 3 cm and r = 2 cm, then
• Arc Length
From our definition of the radian, we have:
s = rθ
For example:
If θ = 2.1 radians and r = 3 cm
Length of arc AB, s = rθ
= 3 × 2.1 cm
= 6.3 cm
• Example 1
The diagram shows part of a circle, centre O, radius r cm. Calculate:
The value of r,
In the sector AOB, s = 2.4 cm and θ= 1.2 radians
In the sector BOC, s = 1.4 cm and r= 2 cm
• Area of a Sector
In the diagram, the angle of the sector AOB is θradians.
By proportion:
r
A
s
Let the area of sector AOB be A.
Thus,
r
Now, as s = rθ, we have:
• Example 2
In the diagram, arc Ab and CD are arc of concentric circles, centre ). If OA = 6 cm, AC = 3 cm and the area of sector AOB is 12 cm2, calculate
The area and perimeter of the shaded region.
Let be AOB = θ radians
Area of the sector AOB = 12 cm2
(b) Now OC = OA + AC = 9 cm