Mensuration
Find the surface area and volume of cylinders and compound solids, and convert between units of area and volume.
Overview
Year 9 mensuration builds on Year 8 by tackling cylinders in full — including curved surface area — and compound solids made from several shapes. Students also convert between units of area and volume. This consolidates the measurement strand ready for the IGCSE Mensuration topic.
What You Will Learn
- Find the area and circumference of circles
- Find the volume of a cylinder using V = πr²h
- Find the curved and total surface area of a cylinder
- Find the volume and surface area of compound solids
- Convert between units of area (cm², m²) and volume (cm³, m³)
Key Vocabulary
Common Mistakes to Avoid
- Using the diameter instead of the radius in a circle or cylinder formula
- Forgetting the two circular ends when finding the total surface area of a cylinder
- Adding instead of subtracting volumes for a hole in a compound solid
- Converting area or volume units using the linear factor instead of its square or cube
What Comes Next
At IGCSE this extends to spheres, cones and pyramids, arcs and sectors, and similar-shape area and volume, within the Mensuration topic.
Frequently Asked Questions
How do I find the surface area of a cylinder?
A cylinder has two circular ends and one curved surface. The curved surface area is 2πrh and each end is πr², so the total surface area is 2πr² + 2πrh. Add all three parts together.
Why is 1 m² not 100 cm²?
Because area is two-dimensional. 1 m = 100 cm, so 1 m² = 100 × 100 = 10 000 cm². For area you square the conversion factor, and for volume you cube it (1 m³ = 1 000 000 cm³).
Study This Topic
Topic Details
- Stage
- Year 9
- Strand
- Geometry and Measure
- Framework ref
- 9Gg
- Difficulty
- High
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) →