Year 10 - Maths
Area of a sector
2D and 3D shape: compound shapes
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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, knowledge of circles and polygons is drawn upon to find the arc length and area of a circle sector and areas of complex compound shapes.
Lesson Summary
You will learn to calculate the area of a sector.
Key Notes
- 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.
Vocabulary To Learn
- 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.
Common Mistakes To Avoid
- If I double the radius of a sector, its area also doubles.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
Using fractions, you can calculate the area of a sector of a circle. An exact answer may be given in terms of π.
2. Use this key word in a maths sentence and explain it clearly. 'Sector'
A sector is the region formed between two radii and their connecting arc. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: If I double the radius of a sector, its area also doubles. Correction: 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°.
More Lessons In This Unit
- Area of compound shapes Study Guide
- Calculating arc length Study Guide
- Checking and securing understanding of area for compound shapes Study Guide
- Checking and securing understanding of area for standard shapes Study Guide
- Checking and securing understanding of circles Study Guide
- Checking and securing understanding of converting between metric and imperial measures Study Guide
- Checking and securing understanding of perimeter for compound shapes Study Guide
- Checking and securing understanding of perimeter for standard shapes Study Guide
- Checking and securing understanding of scales and conversion Study Guide
- Equations from complex shapes Study Guide
- Perimeter and area in a contextual setting Study Guide
- Problem solving with 2D shapes Study Guide
- Problem solving with complex 2D shapes Study Guide
- Shapes on coordinate grids Study Guide
- Shapes within shapes Study Guide
Browse all guides in the Year 10 Maths guide library.