New
New
Lesson 10 of 12
New
New
- Year 10
Area of a sector
I can calculate the area of a sector.
Lesson details
Key learning points
- Using fractions, you can calculate the area of a sector of a circle.
- An exact answer may be given in terms of π
- 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 (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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Prior knowledge starter quiz
6 Questions
Q1.The diameter of a circle is 30 cm. Which of the following statements about this circle are correct?
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.
Its circumference is 30$$\pi$$ cm.
Correct answer: Its area is 225$$\pi$$ cm².
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 .
The perimeter of this shape is 108 cm. The value of $$y$$ is .
Correct Answer: 9, 9 cm, 9cm
9, 9 cm, 9cm
Q3.Which of these statements are correct for this trapezium?
Which of these statements are correct for this trapezium?
The perimeter is 20 cm.
Correct answer: The perimeter is 26 cm.
The perimeter is 26 cm.
The perimeter is 30 cm.
Correct answer: The area is 32 cm².
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 $$x$$?
The perimeter of this shape is 48 cm. Which of these equations can be used to find the value of $$x$$?
Correct answer: 48 = 9 + 13 + 12 + $$x$$
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
$$x$$ = 48 − 9 − 13 − 12
Q5.The perimeter of this trapezium is 48 cm. The area of the trapezium is cm².
The perimeter of this trapezium is 48 cm. The area of the trapezium is cm².
Correct Answer: 138, 138 cm²
138, 138 cm²
Q6.The arc length of this sector is cm (correct to 1 d.p.)
The arc length of this sector is cm (correct to 1 d.p.)
Correct Answer: 56.5, 56.5 cm
56.5, 56.5 cm
Assessment exit quiz
6 Questions
Q1.The sector comes from this circle. The area of the sector is cm².
The sector comes from this circle. The area of the sector is cm².
Correct Answer: 120, 120 cm²
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.
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
42, 42 cm²
Q3.Use the ratio table to identify which of these expressions and values are correct for the area of this sector.
Use the ratio table to identify which of these expressions and values are correct for the area of this sector.
$$255\times 28^2 \pi$$
Correct answer: $${255\over 360}\times 28^2 \pi$$
$${255\over 360}\times 28^2 \pi$$
$$255\times 784 \pi$$
Correct answer: $${255\over 360}\times 784 \pi$$
$${255\over 360}\times 784 \pi$$
Correct answer: 1744.6 cm² (1 d.p.)
1744.6 cm² (1 d.p.)
Q4.Which of these statements are correct about this shape?
Which of these statements are correct about this shape?
The shape is a segment of a circle.
Correct answer: The area is $${80\over360}\times30^2\pi$$ cm².
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).
The area is 600 cm² (nearest 100 cm²).
Correct answer: The shape is a sector of a circle.
The shape is a sector of a circle.
Q5.The area of this sector is cm² (correct to 2 d.p.)
The area of this sector is cm² (correct to 2 d.p.)
Correct Answer: 422.37, 422.37 cm²
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.
The area of sector A is 20 cm². Sector B is similar to sector A. The area of sector B is cm².
Correct Answer: 125, 125 cm²
125, 125 cm²
