Sec 3 G1 Maths Sectors and arcs worksheet with answers

A free Sec 3 G1 Maths worksheet on sectors and arcs: 11 questions, 30 marks, short questions first and then structured ones, in the school exam style. The answers and full worked solutions are on the last page.

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Sec 3 G1 Maths worksheet: Sectors and arcs

Total: 30 marksSuggested time: 50 minutes

Name: ______________________________Class: ____________ Date: ____________

Answer all questions. Show all your working. Give non-exact answers correct to 3 significant figures, or 1 decimal place for angles in degrees, unless the question says otherwise.

Section A

A sector of a circle has radius

7

cm and angle

72^\circ

. Find its area, correct to 3 significant figures.

Answercm²[2]

A sector of a circle has radius

8

cm and angle

210^\circ

. Find the length of its arc, correct to 3 significant figures.

Answercm[2]

A sector of a circle has radius

7

cm and angle

120^\circ

. Find its area, correct to 3 significant figures.

Answercm²[2]

A sector of a circle has radius

9

cm and angle

80^\circ

. Find the length of its arc, correct to 3 significant figures.

Answercm[2]

A sector of a circle has radius

5

cm and angle

225^\circ

. Find its area, correct to 3 significant figures.

Answercm²[2]

A sector of a circle has radius

15

cm and angle

80^\circ

. Find the length of its arc, correct to 3 significant figures.

Answercm[2]

A sector of a circle has radius

12

cm and angle

72^\circ

. Find the length of its arc, correct to 3 significant figures.

Answercm[2]

A sector of a circle has radius

10

cm and angle

72^\circ

. Find the length of its arc, correct to 3 significant figures.

Answercm[2]

A sector of a circle has radius

4

cm and angle

36^\circ

. Find its area, correct to 3 significant figures.

Answercm²[2]

Section B

(a)A sector of a circle has radius

9

cm and angle

120^\circ

. Find its area, correct to 3 significant figures.

Answer (a)cm²[2]

(b)A sector of a circle has radius

4

cm and angle

150^\circ

. Find the length of its arc, correct to 3 significant figures.

Answer (b)cm[2]

(c)A sector of a circle has radius

4

cm and angle

300^\circ

. Find its area, correct to 3 significant figures.

Answer (c)cm²[2]

(a)A sector of a circle has radius

4

cm and angle

210^\circ

. Find the length of its arc, correct to 3 significant figures.

Answer (a)cm[2]

(b)A sector of a circle has radius

9

cm and angle

225^\circ

. Find its area, correct to 3 significant figures.

Answer (b)cm²[2]

(c)A sector of a circle has radius

9

cm and angle

40^\circ

. Find the length of its arc, correct to 3 significant figures.

Answer (c)cm[2]

END OF PAPER

Answers and worked solutions

Question 1

Answer:

\phantom{A} = 30.8

cm² (3 s.f.)[2]

A = \dfrac{\theta}{360} \times \pi r^2

\mathstrut A = \dfrac{72}{360} \times \pi(7)^2

A = 30.7876\ldots

\phantom{A} = 30.8

cm² (3 s.f.)

Question 2

Answer:

\phantom{s} = 29.3

cm (3 s.f.)[2]

s = \dfrac{\theta}{360} \times 2\pi r

\mathstrut s = \dfrac{210}{360} \times 2\pi(8)

s = 29.3215\ldots

\phantom{s} = 29.3

cm (3 s.f.)

Question 3

Answer:

\phantom{A} = 51.3

cm² (3 s.f.)[2]

A = \dfrac{\theta}{360} \times \pi r^2

\mathstrut A = \dfrac{120}{360} \times \pi(7)^2

A = 51.3126\ldots

\phantom{A} = 51.3

cm² (3 s.f.)

Question 4

Answer:

\phantom{s} = 12.6

cm (3 s.f.)[2]

s = \dfrac{\theta}{360} \times 2\pi r

\mathstrut s = \dfrac{80}{360} \times 2\pi(9)

s = 12.5663\ldots

\phantom{s} = 12.6

cm (3 s.f.)

Question 5

Answer:

\phantom{A} = 49.1

cm² (3 s.f.)[2]

A = \dfrac{\theta}{360} \times \pi r^2

\mathstrut A = \dfrac{225}{360} \times \pi(5)^2

A = 49.0873\ldots

\phantom{A} = 49.1

cm² (3 s.f.)

Question 6

Answer:

\phantom{s} = 20.9

cm (3 s.f.)[2]

s = \dfrac{\theta}{360} \times 2\pi r

\mathstrut s = \dfrac{80}{360} \times 2\pi(15)

s = 20.9439\ldots

\phantom{s} = 20.9

cm (3 s.f.)

Question 7

Answer:

\phantom{s} = 15.1

cm (3 s.f.)[2]

s = \dfrac{\theta}{360} \times 2\pi r

\mathstrut s = \dfrac{72}{360} \times 2\pi(12)

s = 15.0796\ldots

\phantom{s} = 15.1

cm (3 s.f.)

Question 8

Answer:

\phantom{s} = 12.6

cm (3 s.f.)[2]

s = \dfrac{\theta}{360} \times 2\pi r

\mathstrut s = \dfrac{72}{360} \times 2\pi(10)

s = 12.5663\ldots

\phantom{s} = 12.6

cm (3 s.f.)

Question 9

Answer:

\phantom{A} = 5.03

cm² (3 s.f.)[2]

A = \dfrac{\theta}{360} \times \pi r^2

\mathstrut A = \dfrac{36}{360} \times \pi(4)^2

A = 5.0265\ldots

\phantom{A} = 5.03

cm² (3 s.f.)

Question 10

(a)Answer:

\phantom{A} = 84.8

cm² (3 s.f.)[2]

A = \dfrac{\theta}{360} \times \pi r^2

\mathstrut A = \dfrac{120}{360} \times \pi(9)^2

A = 84.8230\ldots

\phantom{A} = 84.8

cm² (3 s.f.)

(b)Answer:

\phantom{s} = 10.5

cm (3 s.f.)[2]

s = \dfrac{\theta}{360} \times 2\pi r

\mathstrut s = \dfrac{150}{360} \times 2\pi(4)

s = 10.4719\ldots

\phantom{s} = 10.5

cm (3 s.f.)

(c)Answer:

\phantom{A} = 41.9

cm² (3 s.f.)[2]

A = \dfrac{\theta}{360} \times \pi r^2

\mathstrut A = \dfrac{300}{360} \times \pi(4)^2

A = 41.8879\ldots

\phantom{A} = 41.9

cm² (3 s.f.)

Question 11

(a)Answer:

\phantom{s} = 14.7

cm (3 s.f.)[2]

s = \dfrac{\theta}{360} \times 2\pi r

\mathstrut s = \dfrac{210}{360} \times 2\pi(4)

s = 14.6607\ldots

\phantom{s} = 14.7

cm (3 s.f.)

(b)Answer:

\phantom{A} = 159

cm² (3 s.f.)[2]

A = \dfrac{\theta}{360} \times \pi r^2

\mathstrut A = \dfrac{225}{360} \times \pi(9)^2

A = 159.0431\ldots

\phantom{A} = 159

cm² (3 s.f.)

(c)Answer:

\phantom{s} = 6.28

cm (3 s.f.)[2]

s = \dfrac{\theta}{360} \times 2\pi r

\mathstrut s = \dfrac{40}{360} \times 2\pi(9)

s = 6.2831\ldots

\phantom{s} = 6.28

cm (3 s.f.)

Sec 3 G1 Maths Sectors and arcs worksheet with answers

In the print window, choose Save as PDF to download it.

Or practise it online with step-by-step help when you get one wrong.

Section B

(a)A sector of a circle has radius

9

cm and angle

120^\circ

. Find its area, correct to 3 significant figures.

Answer (a)cm²[2]

(b)A sector of a circle has radius

4

cm and angle

150^\circ

. Find the length of its arc, correct to 3 significant figures.

Answer (b)cm[2]

(c)A sector of a circle has radius

4

cm and angle

300^\circ

. Find its area, correct to 3 significant figures.

Answer (c)cm²[2]

Answers and worked solutions

Question 1

Answer:

\phantom{A} = 30.8

cm² (3 s.f.)[2]

A = \dfrac{\theta}{360} \times \pi r^2

\mathstrut A = \dfrac{72}{360} \times \pi(7)^2

A = 30.7876\ldots

\phantom{A} = 30.8

cm² (3 s.f.)

Question 2

Answer:

\phantom{s} = 29.3

cm (3 s.f.)[2]

s = \dfrac{\theta}{360} \times 2\pi r

\mathstrut s = \dfrac{210}{360} \times 2\pi(8)

s = 29.3215\ldots

\phantom{s} = 29.3

cm (3 s.f.)

Question 3

Answer:

\phantom{A} = 51.3

cm² (3 s.f.)[2]

A = \dfrac{\theta}{360} \times \pi r^2

\mathstrut A = \dfrac{120}{360} \times \pi(7)^2

A = 51.3126\ldots

\phantom{A} = 51.3

cm² (3 s.f.)

Question 4

Answer:

\phantom{s} = 12.6

cm (3 s.f.)[2]

s = \dfrac{\theta}{360} \times 2\pi r

\mathstrut s = \dfrac{80}{360} \times 2\pi(9)

s = 12.5663\ldots

\phantom{s} = 12.6

cm (3 s.f.)

Question 5

Answer:

\phantom{A} = 49.1

cm² (3 s.f.)[2]

A = \dfrac{\theta}{360} \times \pi r^2

\mathstrut A = \dfrac{225}{360} \times \pi(5)^2

A = 49.0873\ldots

\phantom{A} = 49.1

cm² (3 s.f.)

Question 6

Answer:

\phantom{s} = 20.9

cm (3 s.f.)[2]

s = \dfrac{\theta}{360} \times 2\pi r

\mathstrut s = \dfrac{80}{360} \times 2\pi(15)

s = 20.9439\ldots

\phantom{s} = 20.9

cm (3 s.f.)

Question 7

Answer:

\phantom{s} = 15.1

cm (3 s.f.)[2]

s = \dfrac{\theta}{360} \times 2\pi r

\mathstrut s = \dfrac{72}{360} \times 2\pi(12)

s = 15.0796\ldots

\phantom{s} = 15.1

cm (3 s.f.)

Question 8

Answer:

\phantom{s} = 12.6

cm (3 s.f.)[2]

s = \dfrac{\theta}{360} \times 2\pi r

\mathstrut s = \dfrac{72}{360} \times 2\pi(10)

s = 12.5663\ldots

\phantom{s} = 12.6

cm (3 s.f.)

Question 9

Answer:

\phantom{A} = 5.03

cm² (3 s.f.)[2]

A = \dfrac{\theta}{360} \times \pi r^2

\mathstrut A = \dfrac{36}{360} \times \pi(4)^2

A = 5.0265\ldots

\phantom{A} = 5.03

cm² (3 s.f.)

Question 10

(a)Answer:

\phantom{A} = 84.8

cm² (3 s.f.)[2]

A = \dfrac{\theta}{360} \times \pi r^2

\mathstrut A = \dfrac{120}{360} \times \pi(9)^2

A = 84.8230\ldots

\phantom{A} = 84.8

cm² (3 s.f.)

(b)Answer:

\phantom{s} = 10.5

cm (3 s.f.)[2]

s = \dfrac{\theta}{360} \times 2\pi r

\mathstrut s = \dfrac{150}{360} \times 2\pi(4)

s = 10.4719\ldots

\phantom{s} = 10.5

cm (3 s.f.)

(c)Answer:

\phantom{A} = 41.9

cm² (3 s.f.)[2]

A = \dfrac{\theta}{360} \times \pi r^2

\mathstrut A = \dfrac{300}{360} \times \pi(4)^2

A = 41.8879\ldots

\phantom{A} = 41.9

cm² (3 s.f.)

Question 11

(a)Answer:

\phantom{s} = 14.7

cm (3 s.f.)[2]

s = \dfrac{\theta}{360} \times 2\pi r

\mathstrut s = \dfrac{210}{360} \times 2\pi(4)

s = 14.6607\ldots

\phantom{s} = 14.7

cm (3 s.f.)

(b)Answer:

\phantom{A} = 159

cm² (3 s.f.)[2]

A = \dfrac{\theta}{360} \times \pi r^2

\mathstrut A = \dfrac{225}{360} \times \pi(9)^2

A = 159.0431\ldots

\phantom{A} = 159

cm² (3 s.f.)

(c)Answer:

\phantom{s} = 6.28

cm (3 s.f.)[2]

s = \dfrac{\theta}{360} \times 2\pi r

\mathstrut s = \dfrac{40}{360} \times 2\pi(9)

s = 6.2831\ldots

\phantom{s} = 6.28

cm (3 s.f.)