Learning Objectives
- identify radius, diameter and height of a cylinder;
- calculate cylinder volume;
- calculate curved and total surface area;
- use a cylinder net;
- solve capacity and missing-dimension problems.
Introduction
This lesson develops Cylinders from meaning and patterns before moving to calculations. Look for what the quantities, shapes or symbols represent, then connect that idea to the method.
Key Notes
Read the definitions and key facts below carefully. Each rule is most useful when you can explain why it fits the situation, not simply recall it.
Visual Exploration
Use the diagrams, tables or examples in this lesson to identify what changes, what stays fixed and which relationship connects the values.
Understanding a Cylinder
Volume
Find the volume of a cylinder with radius 4 cm and height 10 cm.
V=π(4²)(10)=160π≈502.7 cm³.
Surface Area from the Net
Worked Example: Total Surface Area
Radius 3 cm, height 8 cm.
SA=2π(3)(8)+2π(3²)=48π+18π=66π≈207.3 cm².
Open Cylinder
An open cylinder may have only one circular base, so count only exposed surfaces.
🧠 Let’s Think Together
Before calculating, identify the information given, the result required and the mathematical relationship that connects them. Predict whether the answer should be larger, smaller or unchanged, then use that prediction to check the result.
Practice Questions
Foundation- Find the volume of a cylinder with radius 5 cm and height 12 cm.
- Find the curved surface area of a cylinder with radius 4 m and height 7 m.
- Find total surface area for radius 2 cm and height 9 cm.
- A cylinder has volume 392π cm³ and radius 7 cm. Find height.
- A cylindrical tank has radius 0.5 m and height 1.2 m. Find capacity in litres.
- Find surface area of an open-top cylinder with radius 6 cm and height 10 cm.
- A cylinder has total surface area 150π cm² and radius 5 cm. Find height.
✅ Check Your Work
Show practice answers
- 300π≈942.5 cm³.
- 56π≈175.9 m².
- 44π≈138.2 cm².
- 392π=π×49×h, so h=8 cm.
- V=π(0.5²)(1.2)=0.3π≈0.9425 m³≈942.5 L.
- Curved area + one base = 120π+36π=156π cm².
- 150π=2π(5)h+2π(25) → 150=10h+50 → h=10 cm.
Common Mistakes
- Choosing a rule before identifying what the question describes.
- Skipping working or changing notation part-way through a solution.
- Accepting an answer without checking its size, sign or units.
Exam Focus
Show the mathematical relationship you are using, keep notation consistent and give a clear final answer. Use a quick estimate, diagram or inverse operation to check that the result is reasonable.
Summary
- Cylinder volume = πr²h.
- Curved area = 2πrh.
- Total area includes two circular ends.
- Open cylinders require adjusted surface area.