Year 11 - Maths
Forming equations involving complex shape calculations
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 form and solve equations involving complex shapes and solids.
Key Notes
- There are a variety of approaches to calculations involving shapes.
- There are many skills you will need, such as algebraic manipulation and geometrical reasoning.
- Displaced liquids can have their volumes calculated by finding the volume of the solid that displaced the liquid.
Vocabulary To Learn
- Volume: The volume is the amount of space occupied by a closed 3D shape.
- 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.
- 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 or terms in their calculations, even when these are not the lengths required to form an expression for the volume or surface area.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
There are a variety of approaches to calculations involving shapes. There are many skills you will need, such as algebraic manipulation and geometrical reasoning.
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 or terms in their calculations, even when these are not the lengths required to form an expression for the volume or surface area. Correction: Encourage pupils to annotate diagrams to clearly show how the are breaking down a compound shape, and label clearly any new or missing lengths they can determine.
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
- 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
- Volume of composite solids Study Guide
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