Volume measures the amount of 3D space inside a solid shape. It tells you how much the shape can hold — like how much water fills a fish tank or how much air is in a room! Volume is always measured in cubic units like cm³, m³ or mm³.
📦 Cuboid
V = length × width × height Count the unit cubes that fit inside!
🔺 Triangular Prism
V = ½ × base × height × length Area of triangle × length of prism
🏊 Capacity Link
1 cm³ = 1 ml | 1000 cm³ = 1 litre Volume and capacity are closely connected!
📦 Cuboid
V = l × w × h
🔺 Triangular Prism
V = ½bh × l
📐 Any Prism
V = A × l
The Golden Rules:
Rule 1 — Cuboid: V = length × width × height. Multiply all three dimensions together.
Rule 2 — Any prism: V = area of cross-section × length. Find the face area first, then multiply by how long the prism is.
Rule 3 — Units: Always write cubic units (cm³, m³, mm³). If dimensions are in cm, volume is in cm³.
Rule 4 — Missing side: Rearrange! If V = l × w × h, then h = V ÷ (l × w).
Rule 5 — Capacity: 1 cm³ = 1 ml, so 1000 cm³ = 1 litre. Convert volume to capacity easily.
📝 Worked Examples
Study these carefully before trying the practice questions!
Example 1: Volume of a Cuboid
Question: 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 → V = 8 × 5 × 3
Step 3: Calculate → 8 × 5 = 40, then 40 × 3 = 120
Answer: V = 120 cm³
Example 2: Volume of a Triangular Prism
Question: A triangular prism has a triangle base of 6 cm, triangle height of 4 cm, and a length of 10 cm. Find its volume.
Step 1: Find the area of the triangular cross-section → A = ½ × base × height = ½ × 6 × 4 = 12 cm²
Step 2: Multiply by the length → V = 12 × 10 = 120 cm³
Answer: V = 120 cm³
Example 3: Finding a Missing Dimension
Question: A cuboid has volume 180 cm³, length 9 cm and width 4 cm. Find the height.
Step 1: Write the formula → V = l × w × h
Step 2: Substitute what you know → 180 = 9 × 4 × h
Step 3: Simplify → 180 = 36 × h
Step 4: Divide → h = 180 ÷ 36 = 5
Answer: Height = 5 cm
Example 4: Volume and Capacity
Question: A fish tank measures 50 cm long, 30 cm wide and 40 cm deep. How many litres of water does it hold?
Step 1: Find volume in cm³ → V = 50 × 30 × 40 = 60,000 cm³
Step 2: Convert to litres → 1000 cm³ = 1 litre, so 60,000 ÷ 1000 = 60 litres
Answer: The tank holds 60 litres.
🔬 Volume Visualizer
Choose a shape and enter the dimensions to see the volume calculated step by step!
V = 60 cm³
🧩 Drag 1: Build the Cuboid Formula
Drag l, w and h to complete the cuboid volume formula. Watch out — there are extra tiles!
l
w
h
A
b
V =××
🧩 Drag 2: Find the Volume
A cuboid has length 6 cm, width 4 cm and height 5 cm. Drag the correct answers to complete each step.
24
120
60
150
6 × 4 =
24
× 5 =cm³
🧩 Drag 3: Triangular Prism Volume
A triangular prism has: triangle base = 8 cm, triangle height = 3 cm, prism length = 10 cm. Complete the calculation step by step.
12
120
24
240
Area of △ = ½ × 8 × 3 =cm²
V =
12
× 10 =cm³
🧩 Drag 4: Find the Missing Height
A cuboid has volume = 240 cm³, length = 8 cm, width = 5 cm. Find the missing height by completing the steps.
40
6
30
8
l × w = 8 × 5 =
h = 240 ÷
40
=cm
🧩 Drag 5: Match the Units
Drag the correct unit or conversion value to each statement.
cm³
m³
1000
mm³
Volume of a pencil case (small box):
Volume of a room or building:
1 litre = _____ cm³
🧩 Drag 6: Volume to Capacity
A water tank measures 20 cm long, 10 cm wide and 15 cm deep. Complete the steps to find how many litres it holds.
3000
3
300
30
V = 20 × 10 × 15 =cm³
Litres =
3000
÷ 1000 =litres
📝 Practice Questions
Grab your pencil and paper! Show all working out.
Find the volume of a cuboid with length 4 cm, width 3 cm and height 2 cm.
A box is 10 cm long, 5 cm wide and 6 cm tall. What is its volume?
Calculate the volume of a cuboid measuring 7 cm × 7 cm × 7 cm.
A cuboid has length 12 cm, width 4 cm and height 3 cm. Find its volume.
Find the volume of a cuboid: l = 9 m, w = 2 m, h = 5 m.
A triangular prism has a triangle with base 6 cm and height 4 cm. The prism is 8 cm long. Find the volume.
A triangular prism has base 10 cm, height 3 cm and length 7 cm. Calculate its volume.
A cuboid has volume 60 cm³, length 5 cm and width 4 cm. Find the height.
A cuboid has volume 120 m³, length 6 m and height 4 m. Find the width.
A box holds 200 cm³ of water. The base is 10 cm × 5 cm. How tall is the box?
How many litres of water fill a tank that is 40 cm × 25 cm × 20 cm? (1000 cm³ = 1 litre)
A juice carton measures 6 cm × 4 cm × 12 cm. How many ml does it hold? (1 cm³ = 1 ml)
Two cuboids: A is 5 × 4 × 3 cm and B is 6 × 2 × 5 cm. Which has the greater volume?
A cuboid room is 4 m long, 3 m wide and 2.5 m high. What is the volume of the room?
A shape is made from two cuboids. Cuboid 1: 5 × 3 × 2 cm. Cuboid 2: 2 × 2 × 2 cm. Find the total volume.
A triangular prism has a cross-section area of 15 cm² and a length of 9 cm. Find the volume.
Write whether these volumes are more or less than 1 litre: (a) 500 cm³ (b) 1200 cm³ (c) 999 cm³
A cuboid has volume 360 cm³. Its length and width are both 6 cm. Find the height.
A prism has a cross-section area of 24 m² and volume of 192 m³. Find the length of the prism.
A cuboid has dimensions 3 cm × 3 cm × 3 cm. How many of these cubes fit inside a box measuring 9 cm × 6 cm × 3 cm?
Volume of big box = 9 × 6 × 3 = 162 cm³. Small cube = 27 cm³. 162 ÷ 27 = 6 cubes
🔥 Challenge: Volume Word Problems
Show all your working on paper!
A swimming pool is 25 m long, 10 m wide and 2 m deep. Find its volume in m³, then calculate how many litres it holds. (1 m³ = 1000 litres)
A builder needs to fill a concrete slab that is 6 m long, 4 m wide and 0.2 m thick. What volume of concrete is needed?
A chocolate box contains 24 identical chocolates, each a cuboid measuring 3 cm × 2 cm × 1 cm. What is the total volume of all the chocolates?
A shipping container is 12 m long, 2.5 m wide and 2.5 m tall. What is its volume? How many 1 m³ boxes fit inside?
A wedge of cheese is shaped like a triangular prism. The triangular face has a base of 10 cm and height of 8 cm. The cheese is 12 cm long. Find the volume.
A fish tank is 50 cm × 30 cm × 30 cm. It is filled to three-quarters of its height. How many litres of water are in the tank?
Two cuboids are made from the same amount of clay (same volume). Cuboid A has base 6 cm × 4 cm and height 5 cm. Cuboid B has the same base but a different height. Find the volume of A, then find what height cuboid B would need to have if its base is 8 cm × 5 cm.
A L-shaped swimming pool is made from two cuboid sections: Section 1 is 10 m × 6 m × 1.5 m. Section 2 is 5 m × 4 m × 1.5 m. How many litres of water fill the entire pool? (1 m³ = 1000 litres)
A company packs small boxes (3 cm × 2 cm × 5 cm) into a large crate (30 cm × 20 cm × 25 cm). How many small boxes fit in the crate? What percentage of the crate is filled?
Mr Josh is filling a hollow rectangular planter with soil. The planter is 80 cm long, 25 cm wide and 30 cm deep. A bag of soil has a volume of 10,000 cm³. How many full bags does Mr Josh need to buy to fill the planter completely?