Year 11 - Maths
Checking and securing understanding of volume of a cylinder
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 cylinder.
Key Notes
- A cylinder is not a prism but has a similar structure.
- The formula for the volume of a cylinder can be derived by using the formula for a prism.
- This can be used to find the volume of any cylinder.
- Unknown lengths can be found when the volume of a cylinder is known.
Vocabulary To Learn
- 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.
- Volume: Volume is the amount of space occupied by a closed 3D shape.
Common Mistakes To Avoid
- When questions are in context, the height of the cylinder may be described as the depth or length and this can cause some pupils to struggle if they have learned a formula with a particular word.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
A cylinder is not a prism but has a similar structure. The formula for the volume of a cylinder can be derived by using the formula for a prism.
2. Use this key word in a maths sentence and explain it clearly. '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. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: When questions are in context, the height of the cylinder may be described as the depth or length and this can cause some pupils to struggle if they have learned a formula with a particular word. Correction: Remind pupils that the volume of a 3D shape comes from the area of a cross section multiplied by the height or depth. Discuss which length this would be, using a diagram to support.
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 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 a frustum of a cone Study Guide
- Volume of composite solids Study Guide
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