1. Starter
Calculate the area and circumference (or perimeter) of the following shapes. Give your answers correct to 3 significant figures.
A = 38.5 cm²
C = 22.0 cm
A = 56.5 cm²
C = 30.8 cm
A = 9.42 cm²
C = 13.4 cm

3. Answers

4. ¼ of the area of the whole circle
How would you calculate the area of this sector?
6 cm
¼ of the area of the whole circle

5. 1/6 of the area of the whole circle
How would you calculate the area of this sector?
8 cm
60°
1/6 of the area of the whole circle

6. 53 of the area of the whole circle
How would you calculate the area of this sector?
53°
4 cm
53 of the area of the whole circle
360

7. Calculate the area of this sector and the length of its arc.
4 cm
53°
A = 53 x π x 4²
360
= 7.40 cm²
L = 53 x π x 8
360
= 3.70 cm

8. Calculate the area of this sector and the length of its arc.
6.2 m
237°
A = 237 x π x 6.2²
360
= m²
L = 237 x π x 12.4
360
= m

9. r Θ°
Area of sector = _Θ_ x π x r²
360
Length of arc = _Θ_ x π x d
360

10. Checkpoint: Calculate the area of this sector and the length of its arc.
6.5 m
26°
A = 26 x π x 6.5²
360
= 9.59 m²
L = 26 x π x 13
360
= 2.95 m

12. Extension
The diagram shows a pond. The pond is in the shape of a sector of a circle. Toby is going to put edging on the perimeter of the pond. Edging is sold in lengths of 1.75 metres. Each length of edging costs £3.49. Work out the total cost of edging Toby needs to buy.

13. Answers
1a) 16.8cm b) 62.8cm c) 219.9mm
2a) 47.5cm² b) 463.6mm² c) 589.0cm²

14. The length of the arc on this sector is 12. 54 cm
The length of the arc on this sector is cm. Calculate the angle at the centre.
L = Θ_ x π x d
360
2.54 cm
3.2 cm
2.54 = Θ_ x π x 6.4
360
0.396… = Θ_ x π
360
0.126… = Θ_
360
45.5° = Θ

15. The area of this sector is 78.6 mm². Calculate the angle at the centre.
A = Θ_ x π x r²
360
7 mm
28.6 mm²
78.6 = Θ_ x π x 7²
360
1.604… = Θ_ x π
360
0.510… = Θ_
360
183.8° = Θ

16. Extension
The diagram shows a pond. The pond is in the shape of a sector of a circle. Toby is going to put edging on the perimeter of the pond. Edging is sold in lengths of 1.75 metres. Each length of edging costs £3.49. Work out the total cost of edging Toby needs to buy.

17. Answers 3a) 60° b) 140° c) 280° 4a) 70° b) 145° c) 320°
Extension Answer:
£20.94