Year 11 - Maths
The surface area 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 surface area of a cone.
Key Notes
- The slanted surface of a cone can be cut into congruent triangles.
- These form a parallelogram with dimensions of the slanted length and half of the circumference of the base.
- The area of the slanted surface can be written as πrl
- The surface area of the cone is therefore πrl + πr^2
- The slanted length can be calculated from the height of the cone and radius of the base
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.
- Apex: The apex is the point (vertex) which is the greatest perpendicular distance from the base.
Common Mistakes To Avoid
- When finding the surface area of the cone, pupils may find the curved surface area but forget to include circular base 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 slanted surface of a cone can be cut into congruent triangles. These form a parallelogram with dimensions of the slanted length and half of the circumference of the base.
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: When finding the surface area of the cone, pupils may find the curved surface area but forget to include circular base of the cone. Correction: By re-reading the question, and inspecting any given diagram, pupils can check if the cone is open or closed and therefore if they need to include the circular base in their calculation.
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 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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