Year 11 - Maths
The volume of a pyramid
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 pyramid.
Key Notes
- There are many different types of pyramid.
- The apex of the pyramid is not necessarily above the centre of the base.
- The formula for the volume of a pyramid can be derived.
Vocabulary To Learn
- Pyramid: A pyramid is a 3D shape that has a polygonal base and triangular faces that meet at an apex.
- Apex: The apex is the point (vertex) which is the greatest perpendicular distance from the base.
- Right pyramid: When the apex lies directly above the centre of the base, then it is called a right pyramid.
- Oblique pyramid: An oblique pyramid is when the apex is not directly above the centre of the base.
Common Mistakes To Avoid
- Pupils may use the edge length as the perpendicular height when calculating the volume.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
There are many different types of pyramid. The apex of the pyramid is not necessarily above the centre of the base.
2. Use this key word in a maths sentence and explain it clearly. 'Pyramid'
A pyramid is a 3D shape that has a polygonal base and triangular faces that meet at an apex. 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 use the edge length as the perpendicular height when calculating the volume. Correction: Remind pupils that for any volume calculation, three perpendicular lengths are multiplied and in most pyramids the edge of a triangle is not perpendicular to the base. Also the edge of the triangles can be different in the pyramid.
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 sphere Study Guide
- Volume of a frustum of a cone Study Guide
- Volume of composite solids Study Guide
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