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Measurement - Calculating the volume of cuboids

Grade 5IGCSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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A cuboid is a 3D shape (solid) with six rectangular faces.

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Volume measures the amount of 3D space an object occupies.

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Volume is measured in cubic units, such as cm3cm^3, m3m^3, or mm3mm^3.

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A cube is a special type of cuboid where the length, width, and height are all equal.

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The volume of a cuboid can also be thought of as 'layering' the base area throughout its height.

📐Formulae

Volume of a cuboid=length×width×height\text{Volume of a cuboid} = \text{length} \times \text{width} \times \text{height}

V=l×w×hV = l \times w \times h

Volume=Area of the base×height\text{Volume} = \text{Area of the base} \times \text{height}

Volume of a cube=s×s×s=s3\text{Volume of a cube} = s \times s \times s = s^3 (where ss is the side length)

💡Examples

Problem 1:

Find the volume of a rectangular box that is 8 cm8\text{ cm} long, 5 cm5\text{ cm} wide, and 3 cm3\text{ cm} high.

Solution:

V=8×5×3=120 cm3V = 8 \times 5 \times 3 = 120\text{ cm}^3

Explanation:

To find the volume, multiply the length (8 cm8\text{ cm}), the width (5 cm5\text{ cm}), and the height (3 cm3\text{ cm}). Remember to include the units as cubic centimeters.

Problem 2:

A cuboid has a base area of 42 cm242\text{ cm}^2 and a height of 10 cm10\text{ cm}. What is its volume?

Solution:

V=42×10=420 cm3V = 42 \times 10 = 420\text{ cm}^3

Explanation:

If the area of the base is already given, you simply multiply that area by the height of the cuboid to find the total volume.

Problem 3:

The volume of a cuboid is 60 m360\text{ m}^3. If the length is 5 m5\text{ m} and the width is 4 m4\text{ m}, find the height.

Solution:

Height=60÷(5×4)=60÷20=3 m\text{Height} = 60 \div (5 \times 4) = 60 \div 20 = 3\text{ m}

Explanation:

First, find the area of the base by multiplying length and width (5×4=205 \times 4 = 20). Then, divide the total volume by this area to find the missing height.