Year 11 - Maths
Volume 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 volume of a composite solid.
Key Notes
- A composite solid can be decomposed to make the volume easier to calculate.
- Completing the solid may be a more useful method.
- Decomposing and rearranging parts of the solid may be beneficial.
Vocabulary To Learn
- Volume: The volume is the amount of space occupied by a closed 3D shape.
- 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 only using given measures in their calculations, even when these are not the lengths required for substitution into a volume formula.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
A composite solid can be decomposed to make the volume easier to calculate. Completing the solid may be a more useful method.
2. Use this key word in a maths sentence and explain it clearly. 'Volume'
The volume is the amount of space occupied by a closed 3D shape. 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 only using given measures in their calculations, even when these are not the lengths required for substitution into a volume formula. Correction: Encourage pupils to annotate diagrams to show how the are breaking down a compound/composite shape. Pupils should label the diagram with any new lengths needed. They may need to use Pythagoras or trigonometry to find these new lengths.
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
- Surface area of composite solids 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
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