Year 11 - Maths
The volume of a sphere
2D and 3D shape: surface area and volume (pyramids, spheres and cones)
Study Hub
Study Guides
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 sphere.
Key Notes
- The volume of a sphere can be found by displacement.
- Putting a sphere into a cylinder filled with water displaces the water.
- When the sphere is removed, the water level drops.
- The volume of the sphere is the difference between the volume of the cylinder and water.
- There is a formula you can use to calculate the volume of a sphere.
Vocabulary To Learn
- Sphere: A sphere is a 3D shape, where every point on its surface is equidistant from the centre.
Common Mistakes To Avoid
- Pupils may multiply the radius of the sphere by the constant before cubing it.
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 sphere can be found by displacement. Putting a sphere into a cylinder filled with water displaces the water.
2. Use this key word in a maths sentence and explain it clearly. 'Sphere'
A sphere is a 3D shape, where every point on its surface is equidistant from the centre. 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 multiply the radius of the sphere by the constant before cubing it. Correction: Remind pupils of the order of operations and the need to cube the radius before multiplying by the constants in the formula.
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
- Volume of a frustum of a cone Study Guide
- Volume of composite solids Study Guide
Browse all guides in the Year 11 Maths guide library.