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Year 8

Area of a circle

I can understand the derivation of the area of a circle.

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New
New
Year 8

Area of a circle

I can understand the derivation of the area of a circle.

Download all resources
Share activities with pupils

Lesson details

Key learning points

  1. A circle can be cut into congruent sectors that are placed together to make a parallelogram.
  2. The length of the parallelogram is half the circumference of the circle.
  3. The height of the parallelogram is the radius of the circle.
  4. The formula for the area of a circle can be derived from the area of this parallelogram.

Common misconception

Pupils may confuse the formula for area with the 2πr version of the formula for circumference.

Area is a 2-dimensional space so its formula requires the multiplication of two lengths. This happens when we square the radius.

Keywords

  • Area - Area is the size of the surface and states the number of unit squares needed to completely cover that surface.

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

  • Diameter - The diameter of a circle is any line segment that starts and ends on the edge of the circle and passes through the centre.

In Task A, encourage pupils to compare their answers for questions 1 and 2 to see if their ranges are similar. If pupils are familiar with converting answers to decimals, they could also compare these with question 1 (a) and (b) in Task B.
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).

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Starter quiz

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6 Questions

Q1.
The is any line segment that joins the centre of a circle to its edge.
Correct Answer: radius
Q2.
Which of the following formulae calculates the circumference of a circle, when the radius is known?
$$C=$$ $$1 \over 2$$ $$\pi r$$
$$C = \pi r$$
Correct answer: $$C = 2\pi r$$
Q3.
Which two calculations could be used to find the area of the parallelogram?
An image in a quiz
$$a \times b$$
Correct answer: $$a \times c$$
$$a \times d$$
$$b \times c$$
Correct answer: $$b \times d$$
Q4.
The area of the shape is m$$^2$$.
An image in a quiz
Correct Answer: 16, sixteen
Q5.
The first four digits of $$\pi$$ are .
Correct answer: 3.141
3.142
4.143
4.145
Q6.
Select the parallelogram with the smallest area.
Correct Answer: An image in a quiz
An image in a quiz
An image in a quiz
An image in a quiz

Exit quiz

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6 Questions

Q1.
Which is a correct formula for calculating the area of a circle?
$$A = \pi d$$
$$A = \pi d^2$$
$$A = \pi 2r$$
Correct answer: $$A = \pi r^2$$
Q2.
The area of the circle is equal to the area of the parallelogram. The circumference of the circle is 12$$\pi$$ cm. The base of the parallelogram is .
An image in a quiz
Correct answer: 6$$\pi$$ cm
12$$\pi$$ cm
24$$\pi$$ cm
Q3.
The area of the square is 10 cm. The area of the circle is .
An image in a quiz
Correct answer: 10$$\pi$$ cm$$^2$$
20$$\pi$$ cm$$^2$$
100$$\pi$$ cm$$^2$$
400$$\pi$$ cm$$^2$$
Q4.
A circle has radius 6 cm. What is the area of the circle?
6$$\pi$$ cm$$^2$$
12$$\pi$$ cm$$^2$$
Correct answer: 36$$\pi$$ cm$$^2$$
144$$\pi$$ cm$$^2$$
Q5.
Which circle has an area of 9$$\pi$$ cm$$^2$$?
An image in a quiz
Correct Answer: An image in a quiz
An image in a quiz
An image in a quiz
An image in a quiz
Q6.
The area of the circle is $$\pi$$ cm$$^2$$.
An image in a quiz
Correct Answer: 81, eighty one