Mensuration — Year 9 Revision Notes
These notes cover circles and cylinders, the surface area of a cylinder, compound solids and converting units of area and volume — all at Year 9 (Stage 9) level.
Circles and cylinders
The circumference of a circle is C = πd and its area is A = πr². The volume of a cylinder is V = πr²h. Always use the radius (half the diameter) in these formulas, and the π button or 3.14.
Key Facts & Formulas
- C = πd
- A = πr²
- Cylinder V = πr²h
Tips
- Use the radius, not the diameter, in the formulas.
- Volume is in cubic units.
Surface area of a cylinder
A cylinder's total surface area is made of two circular ends and one curved surface: 2πr² + 2πrh. The curved surface alone is 2πrh. Sketch the net — two circles and a rectangle — to see where each part comes from.
Key Facts & Formulas
- Curved surface = 2πrh
- Total surface = 2πr² + 2πrh
Tips
- Do not forget the two ends for total surface area.
- Curved surface area uses 2πrh only.
Compound solids and unit conversion
Break a compound solid into simple solids, find each volume, then add — or subtract for a hole. For units, area uses the square of the conversion factor and volume the cube: 1 m² = 10 000 cm² and 1 m³ = 1 000 000 cm³.
Key Facts & Formulas
- 1 m² = 10 000 cm²
- 1 m³ = 1 000 000 cm³
Tips
- Split a compound solid into parts you know.
- Square the factor for area, cube it for volume.
Revision Checklist
- I can find the area and circumference of a circle
- I can find the volume of a cylinder
- I can find the curved and total surface area of a cylinder
- I can convert between units of area and volume
Frequently Asked Questions
How do I find the volume of a compound solid?
Split it into simple solids whose volumes you can find, such as a cuboid and a cylinder, then add the volumes together. If part has been cut out, subtract that volume instead.
Build strong foundations in Mensuration
A free trial class with Teacher Rig helps your Year 9 child master Mensuration now — so IGCSE Maths feels familiar, not frightening, later.
Heading toward IGCSE? See how Mensuration develops in IGCSE Mensuration (Cambridge 0580) →