8.6 More Volume and Surface Area

A free GCSE Maths Foundation lesson for Edexcel (9–1) from OBA School: converting units of volume and capacity, and solids made from cuboids. Watch the video, read the explanation and worked examples, then try the revision questions. You can work through the full lesson, with interactive activities, practice quizzes and printable worksheets, in our free online course.

What you will learn

• Convert between mm³, cm³ and m³
• Convert between units of volume and capacity (ml and litres)
• Find the volume of a solid made from cuboids
• Find the surface area of a solid made from cuboids and cubes

Key words

• Capacity: How much liquid a container holds. Units: ml, litres.
• Millilitre (ml): 1 ml = 1 cm³. 1000 ml = 1 litre.
• Composite solid: A solid made by joining simpler solids, such as two cuboids.
• Hidden face: Part of a face that is covered where two solids are joined. It is not part of the surface area.

Converting units of volume

A 1 cm cube is 10 mm long, 10 mm wide and 10 mm high, so its volume is 10 × 10 × 10 = 1000 mm³. Cube the length conversion!

• cm³ → mm³; Conversion × 1000
• m³ → cm³; Conversion × 1 000 000
• mm³ → cm³; Conversion ÷ 1000
• cm³ → m³; Conversion ÷ 1 000 000

Worked example: volume conversions

(a) 2.5 m³ = 2.5 × 1 000 000 = 2 500 000 cm³
(b) 4500 mm³ = 4500 ÷ 1000 = 4.5 cm³

Answer: 2 500 000 cm³ and 4.5 cm³

Volume and capacity

Key fact: 1 cm³ = 1 ml 1000 cm³ = 1 litre 1 m³ = 1000 litres

Worked example: a water tank

A tank is a cuboid 2 m by 1.5 m by 0.8 m. How many litres does it hold?
Volume = 2 × 1.5 × 0.8 = 2.4 m³. 2.4 × 1000 = 2400 litres

Answer: 2400 litres

Worked example: a juice carton

A carton is 6 cm by 4 cm by 10 cm. Volume = 240 cm³ = 240 ml.

Answer: 240 ml

Volume of composite solids

Split the solid into cuboids, find each volume, then add.

Worked example: two cuboids

A: 6 × 4 × 2 = 48 cm³. B: 2 × 4 × 3 = 24 cm³.
Total = 48 + 24 = 72

Answer: 72 cm³

Surface area of composite solids

Only count faces on the outside. Where two solids touch, those faces are hidden.

Worked example: two cubes joined

Two 2 cm cubes are glued face to face. Each cube has surface area 6 × 4 = 24 cm².
Two faces of 4 cm² are hidden: 24 + 24 − 2 × 4 = 40 cm².
Check: the solid is a 4 × 2 × 2 cuboid: 2 × (8 + 8 + 4) = 40 cm².

Answer: 40 cm²

Worked example: a cube on top of a cuboid

Cuboid 6 × 4 × 1: 2 × (24 + 6 + 4) = 68 cm².
The cube covers 4 cm² of the cuboid’s top, but its own top adds exactly 4 cm² back. So add just the 4 sides of the cube: 4 × 4 = 16 cm².
Total = 68 + 16 = 84

Answer: 84 cm²

Common mistakes

• Using × 100 or × 1000 for m³ → cm³. It is × 1 000 000 (100 × 100 × 100).
• Forgetting that 1 litre = 1000 cm³, not 100 cm³.
• Counting hidden faces when finding the surface area of a composite solid.
• Using lengths in different units in one calculation.

Revision questions

Try these, then check your answers below each one.

Question 1. Convert 4 cm³ to mm³.

Answer: 4000 mm³

Working: 4 × 1000 = 4000 mm³.

Question 2. How many cm³ are there in 3 m³? (Choose from: 300, 30 000, 300 000, 3 000 000.)

Answer: 3 000 000

Working: 3 × 1 000 000 = 3 000 000 cm³.

Question 3. Convert 2500 cm³ to litres.

Answer: 2.5 litres

Working: 2500 ÷ 1000 = 2.5 litres.

Related lessons

• Previous lesson: 8.5 Volume of Prisms
• Next lesson: 9.1 Coordinates
• In this chapter: 8.1 Rectangles, Parallelograms and Triangles
• In this chapter: 8.2 Trapezia and Changing Units
• In this chapter: 8.3 Area of Compound Shapes

Continue in the full course

This lesson is section 8.6 (EGCMF0806) of our free GCSE Maths Foundation course. In the full course you get every video for this section, an animated interactive lesson, a self-marking practice quiz, a printable worksheet with a mark scheme, and your progress saved. Go to the full GCSE Maths Foundation course.