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Maths

Volume and Surface Area of Prisms

Overview

Using real objects and nets, students build the conceptual distinction between volume (space inside) and surface area (total outside area), then apply formulae to various prisms.

Learning Objective
Students calculate the volume and surface area of cuboids and triangular prisms, understanding the difference between the two measures.

Resources needed

  • Cereal box or similar cuboid (optional)
  • Centimetre squared paper for nets
  • Calculator

Lesson stages

0 / 7 done
  1. 1 Hold up a box. 'Volume tells us how much it can hold. Surface area tells us how much cardboard was needed to make it.' Pose: 'If I unwrap this box flat, the total area of all the faces is the surface area.'
  2. 2 Volume = length × width × height. Demonstrate with 4cm × 3cm × 2cm cuboid. V = 24cm³. Students calculate volume of three more cuboids. Units: always cubic (cm³, m³).
  3. 3 A cuboid has 6 faces in 3 pairs. Draw a net. Identify the three pairs of rectangles. SA = 2(lw + lh + wh). Calculate for 4×3×2: 2(12+8+6) = 2(26) = 52cm². Students verify by adding all 6 face areas individually.
  4. 4 A prism has a constant cross-section. Volume = area of cross-section × length. For a triangular prism with a triangle base (b=6cm, h=4cm, triangle area=12cm²) and length 10cm: V = 12×10 = 120cm³.
  5. 5 5 faces: 2 triangles + 3 rectangles. Identify each face's dimensions carefully. Calculate each area and sum. Provide a diagram with all measurements labelled.
  6. 6 A swimming pool is a prism (trapezoid cross-section) — find its volume in litres. A gift box is a cuboid — find how much wrapping paper is needed (surface area). Students choose appropriate formula.
  7. 7 A cube has surface area 96cm². Find its volume. (Each face = 16cm², side = 4cm, V = 64cm³.)

Tap a step to mark it as done.

Variations

  • Extend to cylinders (circular cross-section)
  • Compare volumes of different prisms with the same cross-sectional area
  • Include compound prisms (L-shaped cross-section)
More information

Display: volume, surface area, prism, cross-section, net, face, edge, vertex. Use sentence frames: 'The volume is ___ cm³. The surface area is ___ cm².'

Provide net diagrams with faces already labelled. Restrict to cuboids only for those needing more time. Provide formula cards.

Do students use the correct units (cm³ for volume, cm² for surface area)? Do they identify all faces of a prism correctly? Do they apply the cross-section method for non-cuboid prisms?

Draw all 3D shapes on the board. Nets can be drawn on plain paper. All calculations by hand or on a basic calculator.

Students often confuse volume and surface area — return to the physical analogy: 'Volume is the inside space; surface area is how much you need to wrap the outside.'

Activity details
Secondary Medium 45 minutes 10 minutes prep Solo, Pairs Indoor
Topics
Volume Surface Area Prisms 3D Shapes Geometry