Measures and solids · Ages 14–15

Area of a sector worksheet

Part of: Arc lengths & sectors

In the print window, choose “Save as PDF” to download it. The answers print on the last page.

Measures and solids · Ages 14–15

Numsprite
numsprite.com

Name:Date:Score:／48

Write each answer in the space. For word problems, show your working and write a sentence answer.

1.The sector in the picture has a radius of 4 cm and an angle of 135°. What is its area, in terms of π?
Answer:
2.Taking π as 3.14, what is the area of the sector in the picture (radius 12 cm, angle 180°), in cm²?
Answer:
3.Taking π as 3.14, what is the area of the sector in the picture (radius 18 cm, angle 60°), in cm²?
Answer:
4.The sector in the picture has a radius of 15 cm and an arc of 6π cm. What is its area, in terms of π?
Answer:
5.The sector in the picture has a radius of 4 cm and an area of 6π cm². What is its angle at the centre, in degrees?
Answer:
6.The sector in the picture has an angle of 72° and an area of 5π cm². What is its radius, in cm?
Answer:
7.The sector in the picture has a radius of 19 cm and an arc of 34 cm. Its area is cm², and its angle, to the nearest degree, °.
Fill in each blank
Answer:
8.The sector in the picture has a radius of 13 cm and an angle of 200°. Correct to 1 decimal place, what is its area, in cm²?
Answer:
9.The sector in the picture has an angle of 240° and an area of 54π cm². What is its radius, in cm?
Answer:
10.The sector in the picture has a radius of 12 cm and an arc of 7 cm. Its area is cm², and its angle, to the nearest degree, °.
Fill in each blank
Answer:

11.The sector in the picture has a radius of 9 cm and an angle of 120°. What is its area?
- A. 6π cm²
- B. 81π cm²
- C. 27π cm²
- D. 108π cm²
Choose the right answer
Answer:
12.A sector of radius 10 cm and angle 270° has an area of 15π cm².
True or false?
Answer:

13.A flower bed is a sector of radius 3 m with an angle of 90°, and turf costs $45 a square metre. Taking π as 3.14, the bed is m², and the turf costs $ in all.
Fill in each blank
Working:
Answer:
14.A goat is tied by a 6 m rope to one outside corner of a square barn (each side longer than 6 m). The grass it can reach is a 270° sector: π m² in terms of π, and m² taking π as 3.14.
Fill in each blank
Working:
Answer:
15.A pizza of radius 10 cm is cut into 10 equal slices. Each slice has an angle of ° at the centre and an area of π cm².
Fill in each blank
Working:
Answer:
16.A sprinkler waters a sector of radius 12 m with an angle of 100°. Correct to 1 decimal place, what area does it water, in m²?
Working:
Answer:
17.A pizza of radius 18 cm is cut into 6 equal slices. Each slice has an angle of ° at the centre and an area of π cm².
Fill in each blank
Working:
Answer:
18.A flower bed is a sector of radius 3 m with an angle of 60°, and turf costs $65 a square metre. Taking π as 3.14, the bed is m², and the turf costs $ in all.
Fill in each blank
Working:
Answer:

Show the answers and working

Area of a sector worksheet: Answers and working

1. 6 π cm²
Sector area = 135360 × π × 4² = 135360 × 16π = 6π cm².
2. 226.08 cm²
180360 × π × 12² = 72π; with 3.14: 226.08 cm².
3. 169.56 cm²
60360 × π × 18² = 54π; with 3.14: 169.56 cm².
4. 45 π cm²
Sector area = 12 × arc × radius = 12 × 6π × 15 = 45π cm², without finding the angle first (it is 72°).
5. 135°
θ360 × π × 4² = 6π, so θ = 6 × 360 ÷ 4² = 135°.
6. 5 cm
72360 × πr² = 5π, so r² = 5 × 360 ÷ 72 = 25 and r = 5 cm.
7. 323, 103
Area = 12 × 34 × 19 = 323 cm² (no π needed); θ = 34 ÷ (2π × 19) × 360 ≈ 103°.
8. 295 cm²
200360 × π × 13² with the calculator's π, to 1 decimal place: about 295 cm².
9. 9 cm
240360 × πr² = 54π, so r² = 54 × 360 ÷ 240 = 81 and r = 9 cm.
10. 42, 33
Area = 12 × 7 × 12 = 42 cm² (no π needed); θ = 7 ÷ (2π × 12) × 360 ≈ 33°.

Marking: 2 for the working, 1 for the answer, 1 for the sentence.

13. 7.065, 317.925
90360 × 3.14 × 3² = 7.065 m²; 7.065 × 45 = $317.925.
14. 27, 84.78
The barn blocks 90°, leaving 270°: 270360 × π × 6² = 27π; × 3.14 = 84.78 m².
15. 36, 10
360 ÷ 10 = 36°; area 36360 × π × 10² = π × 10² ÷ 10 = 10π cm².
16. 125.7 m²
100360 × π × 12² ≈ 125.7 m².
17. 60, 54
360 ÷ 6 = 60°; area 60360 × π × 18² = π × 18² ÷ 6 = 54π cm².
18. 4.71, 306.15
60360 × 3.14 × 3² = 4.71 m²; 4.71 × 65 = $306.15.

Numsprite · numsprite.com/en/worksheets/arc-lengths-and-sectors/area-of-a-sector