Year 11 - Maths
Checking and securing understanding of volume of prisms
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 prisms.
Key Notes
- The shape and area of the base of a prism can be found.
- The area of the cross-section multiplied by the length gives the volume of the prism.
- This can be used to find the volume of any prism.
- Unknown lengths can be found when the volume of a prism is known.
Vocabulary To Learn
- Volume: Volume is the amount of space occupied by a closed 3D shape.
- Prism: A prism is a polyhedron with a base that is a polygon and a parallel opposite face that is identical. The corresponding edges of the two polygons are joined by parallelograms.
Common Mistakes To Avoid
- When questions are in context, the length may be described as the depth or height and this can cause some pupils to struggle if they have learned a formula with a particular word.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
The shape and area of the base of a prism can be found. The area of the cross-section multiplied by the length gives the volume of the prism.
2. Use this key word in a maths sentence and explain it clearly. 'Volume'
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: When questions are in context, the length may be described as the depth or height and this can cause some pupils to struggle if they have learned a formula with a particular word. Correction: Remind pupils that the volume of a 3D shape comes from a product of three perpendicular lengths. The cross-sectional area uses two of the three, so identify the distance that is perpendicular to the cross-sectional face.
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
- 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
- Volume of composite solids Study Guide
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