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Year 10
Foundation

Area of a sector

I can calculate the area of a sector.

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New
New
Year 10
Foundation

Area of a sector

I can calculate the area of a sector.

Download all resources
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Share activities with pupils
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Lesson details

Key learning points

  1. Using fractions, you can calculate the area of a sector of a circle.
  2. An exact answer may be given in terms of π
  3. Comparisons can be made between the area and another quantity.

Keywords

  • Sector - A sector is the region formed between two radii and their connecting arc.

  • Arc - An arc is part of a curve. An arc of a circle is part of the circle’s circumference.

  • Circumference - The circumference of a circle is the perimeter of the circle.

  • Radius - The radius is any line segment that joins the centre of a circle to any point on its circumference.

Common misconception

If I double the radius of a sector, its area also doubles.

The radius and area of a sector (or circle) do not share a linear relationship, so you cannot apply direct proportional reasoning. However, angle of a sector and its area do share a linear relationship, as long as the angle is ≤ 360°.

Find (get students to find) some real life, current, data for cost of pizza (or other slices that are sectors of a circle). There is lots of space for discussion including how the circle/sector is modelling the situation, how much crust may sway opinion on best value pizza slice etc.
Teacher tip

Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

Lesson video

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Starter quiz

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6 Questions

Q1.
The diameter of a circle is 30 cm. Which of the following statements about this circle are correct?
Its radius is 60 cm.
Its circumference is 15$$\pi$$ cm.
Correct answer: Its circumference is 30$$\pi$$ cm.
Correct answer: Its area is 225$$\pi$$ cm².
Its area is 900$$\pi$$ cm².
Q2.
The perimeter of this shape is 108 cm. The value of $$y$$ is .
An image in a quiz
Correct Answer: 9, 9 cm, 9cm
Q3.
Which of these statements are correct for this trapezium?
An image in a quiz
The perimeter is 20 cm.
Correct answer: The perimeter is 26 cm.
The perimeter is 30 cm.
Correct answer: The area is 32 cm².
The area is 40 cm².
Q4.
The perimeter of this shape is 48 cm. Which of these equations can be used to find the value of $$x$$?
An image in a quiz
Correct answer: 48 = 9 + 13 + 12 + $$x$$
48 + 9 + 13 + 12 = $$x$$
48 = 9 + 13 + 12 − $$x$$
$$x$$ = 48 − 9 + 13 + 12
Correct answer: $$x$$ = 48 − 9 − 13 − 12
Q5.
The perimeter of this trapezium is 48 cm. The area of the trapezium is cm².
An image in a quiz
Correct Answer: 138, 138 cm²
Q6.
The arc length of this sector is cm (correct to 1 d.p.)
An image in a quiz
Correct Answer: 56.5, 56.5 cm

Exit quiz

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6 Questions

Q1.
The sector comes from this circle. The area of the sector is cm².
An image in a quiz
Correct Answer: 120, 120 cm²
Q2.
The area of a circle is 294 cm². The circle is split into 7 congruent sectors. The area of each sector is cm².
Correct Answer: 42, 42 cm²
Q3.
Use the ratio table to identify which of these expressions and values are correct for the area of this sector.
An image in a quiz
$$255\times 28^2 \pi$$
Correct answer: $${255\over 360}\times 28^2 \pi$$
$$255\times 784 \pi$$
Correct answer: $${255\over 360}\times 784 \pi$$
Correct answer: 1744.6 cm² (1 d.p.)
Q4.
Which of these statements are correct about this shape?
An image in a quiz
The shape is a segment of a circle.
Correct answer: The area is $${80\over360}\times30^2\pi$$ cm².
The area is $${400\over9}\pi$$ cm².
Correct answer: The area is 600 cm² (nearest 100 cm²).
Correct answer: The shape is a sector of a circle.
Q5.
The area of this sector is cm² (correct to 2 d.p.)
An image in a quiz
Correct Answer: 422.37, 422.37 cm²
Q6.
The area of sector A is 20 cm². Sector B is similar to sector A. The area of sector B is cm².
An image in a quiz
Correct Answer: 125, 125 cm²