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Year 10
Foundation

Area of a sector

I can calculate the area of a sector.

icon-background-square
New
New
Year 10
Foundation

Area of a sector

I can calculate the area of a sector.

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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°.


To help you plan your year 10 maths lesson on: Area of a sector, download all teaching resources for free and adapt to suit your pupils' needs...

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.
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Licence

This content is © Oak National Academy Limited (2025), 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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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

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