✅ Check: units must be cubic (cm³). If dimensions were in m, answer would be in m³.
Example 2: Volume of a Triangular Prism
A triangular prism has a triangular cross-section with base 9 cm and perpendicular height 6 cm. The prism is 14 cm long. Find its volume.
Step 1: Find the cross-section area: A = ½ × b × h = ½ × 9 × 6 = 27 cm²
Step 2: Multiply by prism length: V = 27 × 14 = 378 cm³
🔺 Always use the perpendicular height of the triangle, not the slant side.
Example 3: Volume of a Cylinder
A cylindrical pipe has diameter 12 cm and length 50 cm. Calculate its volume. Give your answer in terms of π.
Step 1: Find radius: r = 12 ÷ 2 = 6 cm
Step 2: Write formula: V = πr²h = π × 6² × 50
Step 3: Calculate: 6² = 36, then 36 × 50 = 1800
Answer: V = 1800π cm³ ≈ 5654.9 cm³
Example 4: Finding a Missing Dimension
A cuboid has volume 360 cm³. Its length is 12 cm and its width is 5 cm. Find its height.
Step 1: Write formula: V = l × w × h → 360 = 12 × 5 × h
Step 2: Simplify: 360 = 60 × h
Step 3: Solve: h = 360 ÷ 60 = 6 cm
🔍 V ÷ (l × w) = h. Think of it as: if you know the base area and the total volume, dividing gives the height.
🎨 Visualizer
💧 Fill It Up — Water Level Animation
Drag the slider to fill the cuboid. Watch each layer stack up to build the total volume!
5cm
4cm
0cm
Volume filled: 0.0 cm³ | Max: 160.0 cm³
📌 Each 1 cm rise in water = adding one layer of l × w = 20 cm² of cubes!
🏗️ Prism Builder — Pick Your Shape!
Choose a cross-section, set the dimensions with sliders, and see the volume calculate live.
🔬 Unit Conversion Visualiser
One 1 m³ cube contains exactly 1 000 000 cm³. Watch the zoom animation!
1 m³ cube
1 m = 100 cm
1 m³ = 1 000 000 cm³
1 cm³ = 1 ml
🐠 Fish Tank Capacity Calculator
Enter your fish tank dimensions to find the volume, convert to litres, and discover how many fish can live in it!
Length (cm)
×
Width (cm)
×
Height (cm)
🐟 Fun rule: 1 fish needs at least 5 litres of water to be happy and healthy!
✏️ Exercise 1: Volume of Cuboids
Calculate the volume of each cuboid. Give units in your answer.
1. l = 6 cm, w = 4 cm, h = 5 cm → V =
2. l = 10 cm, w = 3 cm, h = 7 cm → V =
3. l = 8 cm, w = 8 cm, h = 8 cm (cube) → V =
4. l = 15 cm, w = 6 cm, h = 4 cm → V =
5. l = 2.5 cm, w = 4 cm, h = 6 cm → V =
6. l = 12 m, w = 5 m, h = 3 m → V =
7. l = 0.5 m, w = 0.4 m, h = 0.2 m → V =
8. A swimming pool: 25 m × 10 m × 2 m → V =
✏️ Exercise 2: Volume of Triangular Prisms
V = ½ × b × h × l (b and h are the base and height of the triangle; l is the prism length)
1. b = 4 cm, h = 3 cm, l = 10 cm → V =
2. b = 6 cm, h = 5 cm, l = 8 cm → V =
3. b = 10 cm, h = 6 cm, l = 12 cm → V =
4. b = 7 cm, h = 4 cm, l = 15 cm → V =
5. b = 9 cm, h = 8 cm, l = 20 cm → V =
6. b = 3 m, h = 2.5 m, l = 6 m → V =
7. b = 12 cm, h = 5 cm, l = 25 cm → V =
8. A triangular roof section: b = 4 m, h = 1.5 m, l = 10 m → V =
✏️ Exercise 3: Volume of Cylinders
V = πr²h Use π ≈ 3.14159 (or the π key). Round to 1 d.p. unless stated.
1. r = 3 cm, h = 10 cm → V = (1 d.p.)
2. r = 5 cm, h = 8 cm → V = (1 d.p.)
3. d = 10 cm (diameter), h = 6 cm → V = (1 d.p.)
4. r = 7 cm, h = 15 cm → V = (1 d.p.)
5. r = 2 m, h = 5 m → V = (1 d.p.)
6. d = 14 cm (diameter), h = 20 cm → V = (1 d.p.)
7. A cylindrical can: r = 4 cm, h = 12 cm → V = (1 d.p.)
8. A pipe: r = 0.5 m, h = 3 m → V = (2 d.p.)
🔍 Exercise 4: Find the Missing Dimension
Use V = l × w × h or V = ½bhl or V = πr²h rearranged to find the unknown.
1. Cuboid: V = 120 cm³, l = 6 cm, w = 4 cm. Find h =
2. Cuboid: V = 360 cm³, l = 10 cm, w = 6 cm. Find h =
3. Cuboid: V = 240 cm³, l = 8 cm, h = 5 cm. Find w =
4. Triangular prism: V = 90 cm³, b = 6 cm, h = 5 cm. Find l =
5. Triangular prism: V = 168 cm³, b = 8 cm, l = 14 cm. Find h =
6. Cylinder: V = 200π cm³, r = 5 cm. Find h =
7. Cylinder: V = 192π cm³, h = 12 cm. Find r =
8. Cuboid room: V = 96 m³, floor 8 m × 6 m. Find ceiling height =
🌍 Exercise 5: Units & Real-World Contexts
1. Convert 2 500 000 cm³ to m³ =
2. Convert 0.35 m³ to cm³ =
3. Convert 4500 cm³ to litres =
4. A fish tank: 50 cm × 25 cm × 30 cm. Volume in cm³ =
5. Same tank: Volume in litres =
6. A swimming pool: 30 m × 12 m × 1.8 m. Volume in m³ =
7. Same pool: Volume in litres (1 m³ = 1000 L) =
8. A cylindrical water tank: r = 0.6 m, h = 1.5 m. Volume in litres (1 d.p.) =
📝 Practice: 20 Mixed Questions
All types mixed. Round decimals to 1 d.p. unless stated.
🏆 Challenge: 8 Hard Questions
Multi-step, reasoning, and problem-solving. Show your working!
C1. A cylinder and a cuboid have the same volume. The cuboid is 10 cm × 8 cm × 6 cm. The cylinder has radius 4 cm. Find the height of the cylinder to 2 d.p.
h =
C2. A triangular prism has volume 270 cm³. The triangular face has base 9 cm. The prism length is 12 cm. Find the perpendicular height of the triangle.
h =
C3. A fish tank (cuboid) holds exactly 120 litres when full. Its base measures 50 cm × 40 cm. Find the height of the tank in cm.
h =
C4. A large cube has side length 1 m. It is cut into small cubes each with side length 5 cm. How many small cubes are made?
Number =
C5. A swimming pool is 20 m long, 8 m wide, and has a sloped floor. One end is 1 m deep, the other is 2.5 m deep. The cross-section is a trapezium. Find the volume in m³. (Area of trapezium = ½(a + b)h, where a and b are the parallel sides)
V =
C6. Two cylinders: Cylinder A has r = 3 cm, h = 8 cm. Cylinder B has r = 6 cm, h = 2 cm. Which has the greater volume and by how much? (give exact answer in terms of π)
Difference = × π cm³ (enter the number only)
C7. A solid metal cuboid (8 cm × 6 cm × 5 cm) is melted and recast into a cylinder of radius 4 cm. Find the height of the cylinder to 2 d.p.
h =
C8. A cuboid box measures 30 cm × 20 cm × 15 cm. Small cubes each with volume 125 cm³ are packed inside. How many cubes fit, and what percentage of the box volume is filled?