Year 11 - Maths
Surface area of composite solids
2D and 3D shape: surface area and volume (pyramids, spheres and cones)
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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 will further develop their understanding of shapes by considering the surface area and volume of pyramids, spheres and cones.
Lesson Summary
You will learn to calculate the surface area of a composite solid.
Key Notes
- The surface area of a composite solid is found by summing the area of all faces.
- The faces may not always be the same shape.
- The surface area may well be able to be calculated in a more efficient way.
Vocabulary To Learn
- Surface area: The surface area is the total area of all the surfaces of a closed 3D shape. The surfaces include all faces and any curved surfaces.
- Solid: A solid is a shape that has three dimensions (e.g. width, height and depth).
- Compound shape: A compound shape is a shape created using two or more basic shapes. A composite shape is an alternative for compound shape.
Common Mistakes To Avoid
- Pupils may not subtract overlapping faces from their surface area calculation.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
The surface area of a composite solid is found by summing the area of all faces. The faces may not always be the same shape.
2. Use this key word in a maths sentence and explain it clearly. 'Surface area'
The surface area is the total area of all the surfaces of a closed 3D shape. The surfaces include all faces and any curved surfaces. 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 not subtract overlapping faces from their surface area calculation. Correction: Ask the pupils to visualise turning around/rotating the compound solid, and consider which faces of the component solids would always be hidden.
More Lessons In This Unit
- Advanced problem solving with further surface area and volume Study Guide
- Checking and securing understanding of nets of solids Study Guide
- Checking and securing understanding of surface area of a cylinder Study Guide
- Checking and securing understanding of surface area of cuboids Study Guide
- Checking and securing understanding of surface area of other prisms Study Guide
- Checking and securing understanding of volume of a cylinder Study Guide
- Checking and securing understanding of volume of prisms Study Guide
- Forming equations involving complex shape calculations Study Guide
- Problem solving with further surface area and volume Study Guide
- Surface area of a frustum of a cone Study Guide
- The surface area of a cone Study Guide
- The surface area of a pyramid Study Guide
- The surface area of a sphere Study Guide
- The volume of a cone Study Guide
- The volume of a pyramid Study Guide
- The volume of a sphere Study Guide
- Volume of a frustum of a cone Study Guide
- Volume of composite solids Study Guide
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