Year 11 - Maths
Volume of a frustum of a cone
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 frustum of a cone.
Key Notes
- The frustum of a cone can be thought of as a cone with the top missing.
- The volume of a frustum of a cone can be thought of as the difference between two cones' volumes.
- This formula can be manipulated to rely on information from the frustum only.
Vocabulary To Learn
- Frustum: A frustum is the 3D shape made from a cone by making a cut parallel to its circular base and removing the resultant smaller cone.
- Volume: Volume is the amount of space occupied by a closed 3D shape.
Common Mistakes To Avoid
- Pupils may think that if you cut the height of the cone in a half, the resulting frustrum will have half the volume of the original cone.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
The frustum of a cone can be thought of as a cone with the top missing. The volume of a frustum of a cone can be thought of as the difference between two cones' volumes.
2. Use this key word in a maths sentence and explain it clearly. 'Frustum'
A frustum is the 3D shape made from a cone by making a cut parallel to its circular base and removing the resultant smaller cone. 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 think that if you cut the height of the cone in a half, the resulting frustrum will have half the volume of the original cone. Correction: The frustrum is actually seven eighths of the volume of the original cone; the small cone that was removed to create the frustrum is one eighth the volume of the original cone if the frustrum and the small cone have the same height.
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 composite solids Study Guide
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