Equal Volume Cuboids
Equal volume questions compare two cuboids that hold the same amount. The key is to calculate the first volume, then use the second cuboid's base area to find the missing dimension.
The Rules Every Equal Volume Question Uses
The papers ask for missing dimensions in cuboids with equal volumes. Most questions use one of three moves: calculate the first volume, divide by a base area, or take the square root of a square base area.
📦 Rule 1: Volume = length × width × height
Start by calculating the volume of the cuboid with all three dimensions given.
Example: 6 × 5 × 2 = 60 cm³.
⚖️ Rule 2: Equal volume means the same cm³
The second cuboid must have exactly the same volume as the first cuboid.
Example: If the first volume is 54 cm³, the second volume is also 54 cm³.
▣ Rule 3: Square base area = side × side
If the base is square, multiply the side length by itself to get the base area.
Example: A square base of side 3 cm has area 3 × 3 = 9 cm².
√ Rule 4: Reverse square area with a square root
If you know the square base area but not the side length, take the square root.
Example: If the base area is 36 cm², the side length is √36 = 6 cm.
How to Solve Equal Volume Questions
Three useful moves: calculate the original volume, divide by the new base area, and use square roots when the missing value is the side of a square base.
1. Find the Height with a Square Base
Question: Two boxes have equal volumes. The first box measures 2 cm by 3 cm by 9 cm. The second has a square base of side 3 cm. What is the height of the second box?
Worked Method
Step 1: Volume of first box = 2 × 3 × 9 = 54 cm³.
Step 2: The second box has the same volume, so it is also 54 cm³.
Step 3: Square base area = 3 × 3 = 9 cm².
Tip: Height = volume ÷ base area, so 54 ÷ 9 = 6 cm.
2. Use a Rectangular Base
Question: A box has dimensions 6 cm by 5 cm by 2 cm. Another box has the same volume, measuring 10 cm long and 2 cm wide. Calculate its height.
Worked Method
Step 1: Volume of first box = 6 × 5 × 2 = 60 cm³.
Step 2: Base area of the second box = 10 × 2 = 20 cm².
Step 3: Height = 60 ÷ 20 = 3 cm.
Tip: For a rectangular base, multiply the two base dimensions before dividing.
3. Find a Square Base Length
Question: A cuboid container has dimensions 3 cm, 24 cm and 3 cm. A second container has the same volume, a square base, and a height of 6 cm. What is the side length of the square base?
Worked Method
Step 1: Volume of first container = 3 × 24 × 3 = 216 cm³.
Step 2: Base area of the second container = 216 ÷ 6 = 36 cm².
Step 3: The base is square, so side length = √36 = 6 cm.
Tip: Do not give 36 cm as the answer. That is the base area; the side length is 6 cm.
Before You Buy
Want to check the level and layout first? Download the free 3-question sample. It uses the same question style, printable format, and answer-key approach as the full pack.
Download Free Sample PDFGet the Full Practice Pack
The full Equal Volume pack contains 90 questions across 3 printable test sets. Students practise cuboid volume, square bases, rectangular bases, missing heights, and missing square base lengths.
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