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.
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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
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What is the volume of a cube with side length ?
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The volume of a cube is calculated as length × length × length. For a side length of , the volume is .
What is its volume?
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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?
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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?
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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?
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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?
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The volume of the cuboid is . The volume of the cube is . The total volume is .
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Volume of a Cuboid and Cube frequently asked questions
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.