Solids and volume

A solid is a 3D shape: a box, a tent, a can, a pyramid. In this topic you'll learn to show solids on flat paper with nets, 3D drawings and views from different sides, and to measure how much space they take up. You'll count cubes, convert between units of volume and capacity, use a rule for the volume of any prism, and explore what happens to a formula's result when you change one measurement. Builders, packers, farmers and engineers use these ideas every day.

What you'll learn

• 13.01 Nets of solids: prisms and pyramids, faces, edges and vertices, and flat nets that fold up into solids.
• 13.02 Visualise solids: isometric drawings, plans with numbers, top, front and side views, and cross-sections.
• 13.03 Volume using unit cubes: volume as the number of cubes inside, counted layer by layer.
• 13.04 Units of volume: mm³, cm³ and m³, capacity in mL, L and kL, and converting between them.
• 13.05 Volume of right prisms: the rule V = A × l for rectangular, triangular and composite prisms.
• 13.06 Attributes in measurement formula: using tables and spreadsheets to see how changing a length, width or height changes the volume.

Which level should I pick?

Every worksheet comes in three levels. Each one covers the same skills.

• Level 1 · Warm-up: whole numbers, labelled diagrams and more help along the way. A good place to start.
• Level 2 · Core: the main worksheet for the lesson.
• Level 3 · Challenge: decimals, mixed units, hidden cubes and problems with more steps, for when the Core level feels easy.

Not sure? Start with Level 2. If the first few questions feel tricky, drop to Level 1. If you finish quickly and get them right, try Level 3. Download the worksheet, print it, and write your answers in the boxes.

Practice tests

When you've finished the lessons, try the three practice tests. Each one is like the real topic test: 45 minutes, 40 marks, a section without a calculator and a section with one. Write your working under each question, then copy your final answers onto the answer sheet on the last page, just like you will in the real test.