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Year 10
Foundation

Checking and securing understanding of circles

I can identify the parts of a circle and calculate the perimeter and area of a circle.

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New
New
Year 10
Foundation

Checking and securing understanding of circles

I can identify the parts of a circle and calculate the perimeter and area of a circle.

Download all resources
Share activities with pupils

Lesson details

Key learning points

  1. A chord splits the circle into two uneven pieces.
  2. The smaller piece is the minor segment and the larger is the major segment.
  3. Sectors look familiar as you broke a circle into sectors to draw a pie chart.
  4. The circumference of a circle is found using C = πd or C = 2πr
  5. The area of a circle is found using A = πr²

Common misconception

"Any line segment starting from the centre of a circle is a radius."

It is true that one endpoint of a radius must be at the centre of a circle. However, the other endpoint must be on the circumference of the circle. This second endpoint cannot be inside or outside of the circle.

Keywords

  • Chord - A chord is any line segment joining two points on the circumference of a circle.

  • Segment - Two segments are created when dividing a circle into two parts using a chord.

  • 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.

Calculators will often give the answer in terms of pi. It is useful to be able to understand when this form is helpful for accuracy or context and when a decimal form may be preferable. Make sure students are confident to convert between these forms.
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.
Which of these shapes are polygons?
An image in a quiz
Correct answer: A
B
C
D
Correct answer: E
Q2.
Which of these statements correctly explains why this shape is not a polygon?
An image in a quiz
It has more than three sides.
It is 2D.
Polygons are 3D shapes.
Correct answer: It is made up of more than just straight-line segments.
Three of its line segments intersect at a perpendicular right-angle.
Q3.
1 centilitre equals $$1 \over 100$$ litres. Match each letter in the ratio table to its value to convert 4040 cl into litres.
An image in a quiz
Correct Answer:$$a$$,$$1 \over 100$$

$$1 \over 100$$

Correct Answer:$$b$$,4040

4040

Correct Answer:$$c$$,40.4

40.4

Q4.
0.065 litres = centilitres.
Correct Answer: 6.5, 6.5 cl, 6.5 centilitres
Q5.
The perimeter of this parallelogram is cm.
An image in a quiz
Correct Answer: 64, 64 cm
Q6.
The area of this parallelogram is cm².
An image in a quiz
Correct Answer: 200, 200 cm², 200 cm squared

Exit quiz

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6 Questions

Q1.
Each diagram shows a different part of a circle. Match each part of a circle to its name.
An image in a quiz
Correct Answer:Diagram a,segment

segment

Correct Answer:Diagram b,sector

sector

Correct Answer:Diagram c,chord

chord

Q2.
The length of the diameter of this circle is inches.
An image in a quiz
Correct Answer: 34, 34 inches
Q3.
The circumference of a circle is 150 cm. Which of these statements is correct about the circle?
The radius of the circle is 75 cm.
The diameter of the circle is 300 cm.
The diameter of the circle is 150$$\pi$$ cm.
Correct answer: An arc from this circle must be less than or equal to 150 cm in length.
An arc from this circle must be greater than or equal to 150 cm in length.
Q4.
The diameter of a circle is 60 cm. Which of these statements is correct about the circle?
Correct answer: The radius of the circle is 30 cm.
The radius of the circle is 120 cm.
The circumference of the circle is 30$$\pi$$ cm.
Correct answer: The circumference of the circle is 60$$\pi$$ cm.
The circumference of the circle is 120$$\pi$$ cm.
Q5.
The radius of a circle is 9 cm. Which of these statements is correct about the circle?
The diameter of the circle is 4.5 cm.
Correct answer: The diameter of the circle is 18 cm.
The area of the circle is 9$$\pi$$ cm².
Correct answer: The area of the circle is 81$$\pi$$ cm².
The area of the circle is 255 cm² (to the nearest integer).
Q6.
The area of this circle can be calculated from the equation $$A = \pi \times 62^2$$. Match each property of the circle to its value.
Correct Answer:radius (in cm),62

62

Correct Answer:diameter (in cm),124

124

Correct Answer:circumference (in cm),124$$\pi$$

124$$\pi$$

Correct Answer:area (in cm²),12 076.28

12 076.28