Volume of a Cuboid and Cube
Volume of a cuboid is the space inside it, found by length × width × height. For example, a 5 × 3 × 2 box holds 30 cm³, given in cubic units. A cube is a special cuboid with equal edges, so its volume is side × side × side.
Video Lesson
Watch and learn the basics
🎬 Did this video explain it clearly?
Flashcards
Review key concepts visually
%20Volume%20of%20Cuboids%20an%20Cubes.webp)
%20Volume%20of%20Cuboids%20Calculation.webp)
%20Volume%20of%20Complex%20Solids.webp)
%20Volume%20of%20Cuboid%20Application.webp)
Volume of Cuboids and Cubes
- The volume of a cuboid: Volume = length × width × height.
- The volume of a cube: Volume = side × side × side.
Finding a Missing Dimension
- If the volume of a cuboid and two dimensions are known, the third can be found.
- Use Volume = length × width × height, then divide to find the missing value.
Volume of Compound Solids
- A compound solid can be split into smaller cuboids.
- Find the volume of each part and add them together.
Using Volume in Real Life
- Volume can be used to find capacity, such as how much liquid a container holds.
- You may need to convert units (e.g. from cm³ to litres) when calculating volume.
Practice Questions
Test your understanding
What is the volume of a cube with side length ?
Correct! 🎉 +10 pointsNot quite right
The volume of a cube is calculated as length × length × length. For a side length of , the volume is .
What is its volume?
Correct! 🎉 +10 pointsNot quite right
The volume of a cuboid is calculated as length × width × height. For this cuboid: .
A cube has a volume of . What is the length of one side?
Correct! 🎉 +20 pointsNot quite right
The volume of a cube is length × length × length. To find the side length, take the cube root of 64: cm.
A cuboid has a volume of , with a length of and a width of . What is its height?
Correct! 🎉 +20 pointsNot quite right
The volume of a cuboid is length × width × height. Rearranging for height: height = volume ÷ (length × width). For this cuboid, .
A cuboid has a volume of . Its height is and its width is . What is the length of the cuboid?
Correct! 🎉 +20 pointsNot quite right
The volume of a cuboid is length × width × height. For length: length = volume ÷ (width × height). For this cuboid, .
A compound solid consists of a cuboid and a cube. The cuboid has a length of , a width of , and a height of . The cube has a side length of . What is the total volume of the solid?
Correct! 🎉 +30 pointsNot quite right
The volume of the cuboid is . The volume of the cube is . The total volume is .
Want to see the full working?
Interactive Activity
Explore volume of cubes and cuboids by adjusting dimensions
Loading interactive widget...
Students Also Ask
The questions students bump into most on this topic
The formula for the volume of a cuboid is length × width × height. You multiply the three measurements together and give the answer in cubic units, such as cm³ or m³. For example, a cuboid measuring 5 cm by 3 cm by 2 cm has a volume of 30 cm³.
A cube is a special cuboid with equal edges, so you multiply one edge length by itself three times. For an edge of 5 cm, the volume is 5 × 5 × 5, which equals 125 cm³. The answer is always written in cubic units.
A cuboid is a 3D shape with a length, width, and height that can all differ. A cube is a special cuboid where every edge is the same length. So every cube is a cuboid, but only cuboids with equal edges are cubes.
Volume is measured in cubic units because it fills three dimensions. Common units are cubic centimetres (cm³) and cubic metres (m³). You can also convert between units of volume, for example 1 litre equals 1,000 cubic centimetres, which helps with everyday capacity problems.
Use the formula length × width × height and put in the values you know. Multiply the two known measurements, then divide the volume by that result. For example, if 10 × width × 2 = 120, then 10 × 2 = 20 and 120 ÷ 20 = 6, so the width is 6 m.
Divide the number of cubic centimetres by 1,000, because 1 litre equals 1,000 cubic centimetres. For example, a container with a volume of 30,000 cm³ holds 30,000 ÷ 1,000 = 30 litres. This step is useful when you work out the capacity of a cuboid container.