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Year 8

Using the formula for the area of a circle

I can use the formula for the area of a circle to calculate either the area or a missing measurement.

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Share activities with pupils
New
New
Year 8

Using the formula for the area of a circle

I can use the formula for the area of a circle to calculate either the area or a missing measurement.

Download all resources
Share activities with pupils

Lesson details

Key learning points

  1. The area of any circle can be found if the radius is known.
  2. The radius can be calculated from the diameter.
  3. The area of a circle can be used to calculate the radius .
  4. The area of a circle can be used to calculate the diameter.
  5. For the answer to be exact it needs to be left in terms of π.

Common misconception

When calculating the diameter, pupils may use rounded numbers to perform subsequent calculations.

Repeat one of the demonstrations of finding the diameter but round each decimal as they appear and compare the accuracy of the final answer.

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.

Regularly remind pupils that the radius and diameter can be measured in any direction. This will be particularly helpful in Task A.
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.
Match the parts of a circle with their descriptions.
Correct Answer:circumference,the distance around the edge of a circle

the distance around the edge of a circle

Correct Answer:diameter,furthest distance from one side of a circle to the other

furthest distance from one side of a circle to the other

Correct Answer:radius,any line segment from centre to circumference of circle

any line segment from centre to circumference of circle

Q2.
What is 10$$\pi$$ as a decimal rounded to 3 significant figures?
Correct Answer: 31.4, thirty one point four
Q3.
Evaluate the expression $$5x^2$$ when $$x=2$$.
Correct Answer: 20, twenty
Q4.
Solve the equation: $$4x^2 = 36$$
Correct Answer: 3, three, x = 3, x=3, 3 = x
Q5.
Which is the formula for the area of a circle?
$$A = \pi r$$
$$A = 2\pi r$$
$$A = \pi r2$$
Correct answer: $$A = \pi r^2$$
$$A = \pi^2 r$$
Q6.
What is the area of the circle?
An image in a quiz
$$9 \pi$$ cm$$^2$$
$$18 \pi$$ cm$$^2$$
Correct answer: $$81 \pi$$ cm$$^2$$
$$324 \pi$$ cm$$^2$$

Exit quiz

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6 Questions

Q1.
The area of a circle can be calculated by multiplying $$\pi $$ by the square of the .
Correct Answer: radius
Q2.
A circle has radius 10 cm. Its area is cm$$^2$$, when rounded to 3 significant figures.
Correct Answer: 314, three hundred and forteen
Q3.
The area of the circle is cm$$^2$$.
An image in a quiz
6$$\pi$$
Correct answer: 9$$\pi$$
12$$\pi$$
36$$\pi$$
Q4.
The distance from the centre of a circle to its edge is 12 cm. The area of the circle is $$\pi$$ cm$$^2$$.
Correct Answer: 144, one hundred and forty-four, one hundred and forty four
Q5.
The area of a circle is 80 cm$$^2$$. The radius is cm, when rounded to 3 significant figures.
2.85
Correct answer: 5.05
10.1
25.5
Q6.
The area of a circle is 150 cm$$^2$$. The diameter is cm, when rounded to 3 significant figures.
3.45
6.91
Correct answer: 13.8
47.7