Area of a sector | Maths | Quizalize & Oak National Academy

Starter quiz

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.

Its circumference is 30 $\pi$ cm. ✓

Its area is 225 $\pi$ cm². ✓

Its area is 900 $\pi$ cm².
The perimeter of this shape is 108 cm. The value of $y$ is ______.

'9' ✓
Which of these statements are correct for this trapezium?

The perimeter is 20 cm.

The perimeter is 26 cm. ✓

The perimeter is 30 cm.

The area is 32 cm². ✓

The area is 40 cm².
The perimeter of this shape is 48 cm. Which of these equations can be used to find the value of $x$ ?

48 = 9 + 13 + 12 + $x$ ✓

48 + 9 + 13 + 12 = $x$

48 = 9 + 13 + 12 − $x$

$x$ = 48 − 9 + 13 + 12

$x$ = 48 − 9 − 13 − 12 ✓
The perimeter of this trapezium is 48 cm. The area of the trapezium is ______cm².

'138' ✓
The arc length of this sector is ______ cm (correct to 1 d.p.)

'56.5' ✓

Exit quiz

The sector comes from this circle. The area of the sector is ______ cm².

'120' ✓
The area of a circle is 294 cm². The circle is split into 7 congruent sectors. The area of each sector is ______ cm².

'42' ✓
Use the ratio table to identify which of these expressions and values are correct for the area of this sector.

$255\times 28^2 \pi$

${255\over 360}\times 28^2 \pi$ ✓

$255\times 784 \pi$

${255\over 360}\times 784 \pi$ ✓

1744.6 cm² (1 d.p.) ✓
Which of these statements are correct about this shape?

The shape is a segment of a circle.

The area is ${80\over360}\times30^2\pi$ cm². ✓

The area is ${400\over9}\pi$ cm².

The area is 600 cm² (nearest 100 cm²). ✓

The shape is a sector of a circle. ✓
The area of this sector is ______ cm² (correct to 2 d.p.)

'422.37' ✓
The area of sector A is 20 cm². Sector B is similar to sector A. The area of sector B is ______ cm².

'125' ✓

Worksheet

Loading worksheet ...

Presentation

Loading presentation ...

Video

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.

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°.

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.