Year 11 - Maths
The volume 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 cone.
Key Notes
- The volume of a cone can be found by displacement.
- Putting a cone into a cylinder filled with water displaces the water.
- When the cone is removed, the water level drops.
- The volume of the cone is the difference between the volume of the cylinder and water.
- There is a formula you can use to calculate the volume of a cone.
Vocabulary To Learn
- Cone: A circular cone is a 3D shape that has a circular base and one curved surface that narrows from the base to a fixed point called the apex/vertex.
- Right cone: A line drawn through the apex and centre of the base of a right circular cone will be perpendicular to the base.
- Volume: Volume is the amount of space occupied by a closed 3D shape.
Common Mistakes To Avoid
- Pupils may confuse the slant height (which is needed to find the curved surface area of the cone) with the perpendicular height (which is needed to find the volume of the cone).
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
The volume of a cone can be found by displacement. Putting a cone into a cylinder filled with water displaces the water.
2. Use this key word in a maths sentence and explain it clearly. 'Cone'
A circular cone is a 3D shape that has a circular base and one curved surface that narrows from the base to a fixed point called the apex/vertex. 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 confuse the slant height (which is needed to find the curved surface area of the cone) with the perpendicular height (which is needed to find the volume of the cone). Correction: Remind pupils that for any volume calculation, three perpendicular lengths are multiplied and the slant height is not perpendicular to the base in a right cone. They may need to use Pythagoras' theorem to find the perpendicular 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 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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