Volume of Prisms
This topic covers 4 learning steps, guiding your child from the basics through to confident problem-solving. Each step includes a worked example and adaptive practice questions.
What Your Child Will Learn
- What Is a Prism?
Identify prisms and their cross-sections - Volume = Area of Cross-Section x Length
Use the prism volume formula - Triangular Prisms
Calculate volume of triangular prisms - Challenge — Mixed Prism Problems
Complex volume problems with various prisms
Before This Topic
Your child should be comfortable with:
- Volume of Cuboids (Year 5)
- Area of Triangles (Year 6)
Common Mistakes
- Confusing volume with surface area (calculating the total of all faces rather than the space inside)
Volume measures the space INSIDE a 3D shape — how much water it could hold. Surface area measures the total outside covering. For volume, you multiply the cross-section area by the length. - Using the wrong face as the cross-section (e.g. using the rectangular side of a triangular prism instead of the triangle)
The cross-section is the shape you see when you slice straight through the prism like cutting a loaf of bread. For a triangular prism, the cross-section is the triangle, not the rectangle.
Tips for Parents
- Use a loaf of bread to explain prisms: every slice is the same shape (the cross-section). Volume = area of one slice multiplied by the number of slices (the length).
- Find prisms around the house — a Toblerone box (triangular prism), a cereal box (rectangular prism), a tin of beans (circular prism, also called a cylinder). Ask your child to spot the cross-section.
- Remind your child that the cross-section area formula depends on the shape: rectangle = length x width, triangle = base x height ÷ 2. The prism formula always multiplies that area by the depth.
- Practise estimating volumes of real objects: "How many cubic centimetres do you think this pencil case holds?" Then calculate and compare.
Key Words
- Prism — A 3D shape with the same cross-section all the way through — like a Toblerone box or a tent shape.
- Cross-section — The 2D shape you see when you slice straight through a prism — like the triangle at the end of a Toblerone.
- Volume — The amount of space inside a 3D shape, measured in cubic units like cm³ or m³.
- Cubic centimetre (cm³) — A cube measuring 1 cm on every edge — about the size of a small sugar cube.
- Depth (or length) — How far the cross-section extends through the prism — the distance from front to back.
Where This Fits
Before this topic: Children should know how to find the area of rectangles and triangles, and understand what volume means from working with cubes and cuboids.
After this topic: Volume of prisms leads to calculating volumes of cylinders, cones, and spheres, and to working with composite 3D shapes in later years.
How MathCraft Teaches This
In MathCraft, Volume of Prisms is taught through the Geometry & Shape adventure track. Your child follows guided lessons with friendly characters, works through examples step by step, then practises with questions that adapt to their level.
The adaptive engine tracks mastery across all 4 steps, revisiting concepts your child finds tricky and advancing when they're ready. Parents can see detailed progress in the Parent Dashboard.
Practise Volume of Prisms with MathCraft
Step-by-step lessons, worked examples, and adaptive practice — all wrapped in an adventure game your child will love.
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