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Cambridge Lower Secondary · Year 8 Geometry and Measure · Geometrical reasoning, shapes and measurements

Area, Surface Area & Volume

Find the area and circumference of circles, the area of compound shapes, and the surface area and volume of prisms.

Overview

Building on Year 7's work with rectangles and triangles, Year 8 students learn to work with circles — finding circumference and area using π — and with prisms, finding their volume and surface area. They also tackle compound shapes made from simpler pieces. These mensuration skills appear throughout IGCSE and in real contexts like packaging, capacity and construction.

What You Will Learn

  • Find the circumference of a circle using C = πd
  • Find the area of a circle using A = πr²
  • Find the area of compound shapes made from rectangles, triangles and parts of circles
  • Find the volume of a prism, including a cylinder
  • Find the surface area of a cuboid and other simple prisms

Key Vocabulary

circumferenceradiusdiameterpi (π)prismcross-sectionsurface areavolume

Common Mistakes to Avoid

  • Using the radius instead of the diameter in C = πd (or vice versa)
  • Squaring the diameter instead of the radius in A = πr²
  • Confusing area (cm²) and volume (cm³) units
  • Forgetting a face when adding up the surface area of a solid

What Comes Next

In Year 9 and at IGCSE this extends to spheres, cones and pyramids, and to problems that combine several solids. It forms the IGCSE Mensuration topic.

Frequently Asked Questions

When do I use the radius and when the diameter?

The circumference formula C = πd uses the diameter (the full width). The area formula A = πr² uses the radius (half the diameter). If you are given the diameter, halve it before using the area formula.

How do I find the volume of any prism?

A prism has the same cross-section all along its length, so its volume is the area of that cross-section multiplied by the length: V = cross-sectional area × length. For a cylinder the cross-section is a circle, so V = πr² × height.

Topic Details

Stage
Year 8
Strand
Geometry and Measure
Framework ref
8Gg
Difficulty
Medium

Build strong foundations in Area, Surface Area & Volume

A free trial class with Teacher Rig helps your Year 8 child master Area, Surface Area & Volume now — so IGCSE Maths feels familiar, not frightening, later.

Next step: IGCSE

Heading toward IGCSE? See how Area, Surface Area & Volume develops in IGCSE Mensuration (Cambridge 0580)