Area of a sector
I can calculate the area of a sector.
Area of a sector
I can calculate the area of a sector.
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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°.
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...
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.
The starter quiz will activate and check your pupils' prior knowledge, with versions available both with and without answers in PDF format.
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The assessment exit quiz will test your pupils' understanding of the key learning points.
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Explore more key stage 4 maths lessons from the 2D and 3D shape: compound shapes unit, dive into the full secondary maths curriculum, or learn more about lesson planning.
Licence
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?
Q2.The perimeter of this shape is 108 cm. The value of $$y$$ is .

Q3.Which of these statements are correct for this trapezium?

Q4.The perimeter of this shape is 48 cm. Which of these equations can be used to find the value of $$x$$?

Q5.The perimeter of this trapezium is 48 cm. The area of the trapezium is cm².

Q6.The arc length of this sector is cm (correct to 1 d.p.)

Assessment exit quiz
6 Questions
Q1.The sector comes from this circle. The area of the sector is 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.
Q3.Use the ratio table to identify which of these expressions and values are correct for the area of this sector.

Q4.Which of these statements are correct about this shape?

Q5.The area of this sector is cm² (correct to 2 d.p.)

Q6.The area of sector A is 20 cm². Sector B is similar to sector A. The area of sector B is cm².
