Equal Volume Cuboids Practice Test Worksheets
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.
For students who understand cuboid volume, but lose marks when an equal-volume match hides a missing height or square base length.
Opens in Etsy, which handles checkouts and downloads.
What Do Equal Volume Questions Look Like?
Students are given two cuboids with identical volumes and must determine an unknown height or base dimension. Questions require finding the first volume using length, width, and height, then dividing by the second shape's base area to find the missing measurement. Here is a worked example.
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.
Step 4: Height = volume ÷ base area, so 54 ÷ 9 = 6 cm.
Tip: Check by multiplying the base area by the height: 9 cm² × 6 cm = 54 cm³, matching the first box.
Rules to Help You Solve Equal Volume Questions
As shown in the example above, once you know the total volume of one cuboid, you can work backwards from the second cuboid's base to find its missing dimension. Use these core rules to solve rectangular and square base problems systematically. Diagrams not to scale; use the labelled dimensions when calculating.
📦 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.
Two More Worked Examples
Practise finding a missing height with a rectangular base, then learn how to take a square root to find a square base length.
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.
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: 36 cm² is the base area, not the side length. Take √36 to get 6 cm.
