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RV-25-001 · Sector: derive the angle and compare areas

A sector has radius 18 cm and arc length 11π11\pi cm. A square has side 72 cm.
OAB18 cmθ
Diagram not accurately drawn

(a) Calculate the angle of the sector and its area. Give the area in terms of π.

(b) What percentage of the square’s area is the sector’s area? Give your answer to 1 decimal place.

Part (a) Arcs and Sectors: Reverse Angle & Area Percentage Booklet p. 38 & p. 51
Method
1) Use Arc = (θ/
3
6
0) × 2πr to solve for θ
2) Use Sector Area = (θ/
3
6
0) × πr²
3) Divide sector area by square area and × 100%
Worked Example (RV-25-001 · Part (a))
Calculate the angle of the sector and its area. Give the area in terms of π.
1)
Divide the arc length by the circumference to find the fraction of a circle.
2)
Angle 110°.
3)
Multiply this fraction by πr².
4)
99π99\pi cm²
Ans = 110°; 99π99\pi cm².
Part (b) Arcs and Sectors: Reverse Angle & Area Percentage Booklet p. 38 & p. 51
Method
1) Use Arc = (θ/
3
6
0) × 2πr to solve for θ
2) Use Sector Area = (θ/
3
6
0) × πr²
3) Divide sector area by square area and × 100%
Worked Example (RV-25-001 · Part (b))
What percentage of the square’s area is the sector’s area? Give your answer to 1 decimal place.
1)
Divide sector area by 5184, then multiply by 100.
2)
6.0%
Ans = 6.0%