Knowledge Organiser: Volume of Cuboids & Prisms
Key Terms
- Prism: A 3D shape with a constant cross-section throughout its length
- Cross-section: The identical 2D shape cut through the prism
- Cuboid: A rectangular prism (box shape)
- Cylinder: A circular prism
- Volume: Amount of 3D space a shape occupies: in cubic units
Must-Know Facts
- All prism volumes = cross-sectional area × length
- Volume is ALWAYS in cubic units: cm³, m³, mm³
- Cylinder = circular prism: V = πr²h
- If given diameter, halve it first to get radius
- 1 m³ = 1000 litres; 1 litre = 1000 cm³
- Double all dimensions → volume increases by factor 8 (2³)
Key Formulas
- Any prism: V = A × l
- Cuboid: V = l × w × h
- Cylinder: V = πr²h
- Density: mass = density × volume
Common Mistakes
- Prism cross-section: Must identify the correct cross-section (the face that stays the same along the length)
- Units cubed: Volume is always cm³, m³ etc.: never cm² or cm
- Cylinder vs prism: Cylinder is a circular prism: V = πr²h, not πdh
- Missing the length: For a prism, V = cross-sectional area × length: don't forget to multiply by the length
Worked Examples
Find the volume of a cuboid with length 8 cm, width 5 cm, and height 3 cm. Step 1 Write the formula V = l × w × h Step 2 Substitute and calculate V = 8 × 5 × 3 = 120 cm³
Worked Examples
A triangular prism has a triangle face with base 6 cm and height 4 cm. The prism is 10 cm long. Find its volume. Step 1 Find cross-sectional area (triangle) Area = ½ × base × height = ½ × 6 × 4 = 12 cm² Step 2 Multiply by length V = 12 × 10 = 120 cm³
Worked Examples
A cylinder has radius 4 cm and height 7 cm. Find its volume to 1 decimal place. Step 1 Write the formula V = πr²h Step 2 Square the radius r² = 4² = 16 Step 3 Calculate V = π × 16 × 7 = π × 112 = 351.86... = 351.9 cm³