Year 8 - Maths
Area of a circle
Perimeter, area and volume
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This pupil-friendly study guide includes a unit summary, clear notes, common mistakes, and quick questions with answers.
Unit Summary
In this unit pupils extend their knowledge of shapes by exploring the properties of circles and composite shapes before developing understanding of 3-D shapes including surface area and volume.
Lesson Summary
You will learn to understand the derivation of the area of a circle.
Key Notes
- A circle can be cut into congruent sectors that are placed together to make a parallelogram.
- The length of the parallelogram is half the circumference of the circle.
- The height of the parallelogram is the radius of the circle.
- The formula for the area of a circle can be derived from the area of this parallelogram.
Vocabulary To Learn
- 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.
Common Mistakes To Avoid
- Pupils may confuse the formula for area with the 2πr version of the formula for circumference.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
A circle can be cut into congruent sectors that are placed together to make a parallelogram. The length of the parallelogram is half the circumference of the circle.
2. Use this key word in a maths sentence and explain it clearly. 'Area'
Area is the size of the surface and states the number of unit squares needed to completely cover that surface. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: Pupils may confuse the formula for area with the 2πr version of the formula for circumference. Correction: Area is a 2-dimensional space so its formula requires the multiplication of two lengths. This happens when we square the radius.
More Lessons In This Unit
- Area of composite shapes Study Guide
- Checking understanding of area Study Guide
- Checking understanding of perimeter Study Guide
- Circumference of a circle Study Guide
- Finding a length in composite shapes Study Guide
- Multiplicative relationships in circles Study Guide
- Perimeter of composite shapes Study Guide
- Problem solving with perimeter, area and volume Study Guide
- Properties of prisms Study Guide
- Surface area of cuboids Study Guide
- Surface area of cylinders Study Guide
- Surface area of prisms Study Guide
- Using the formula for the area of a circle Study Guide
- Volume of cylinders Study Guide
- Volume of prisms Study Guide
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