Year 11 - Maths
Problem solving with further surface area and volume
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 use your enhanced knowledge of surface area and volume to solve problems.
Key Notes
- The surface area of many solids can be calculated by a known method.
- The volume of many solids can be calculated by a known method.
- Writing an algebraic statement about surface area/volume can be done from a diagram.
Vocabulary To Learn
- 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.
- Cylinder: A cylinder is a 3D shape with a base that is a circle and a parallel opposite face that is identical. A cross-section of a cylinder made parallel to the base will be congruent to the base.
- Surface area: The surface area is the total area of all the surfaces of a closed 3D shape. The surfaces include all faces and any curved surfaces.
- Volume: Volume is the amount of space occupied by a closed 3D shape.
Common Mistakes To Avoid
- Pupils may confuse whether they need to calculate the volume or surface area of a 3D shape, if not told specifically to do so in a problem.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
The surface area of many solids can be calculated by a known method. The volume of many solids can be calculated by a known method.
2. Use this key word in a maths sentence and explain it clearly. '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. 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 whether they need to calculate the volume or surface area of a 3D shape, if not told specifically to do so in a problem. Correction: Use the context to decide which calculation is needed. If the question refers to packaging or painting the shape, a surface area calculation is needed.
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
- 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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