Compound Cuboid Volume Practice Test Worksheets
Build confidence with printable compound cuboid volume worksheets and focused maths practice tests. Students learn to split stacked solids into cuboids, subtract cut-out sections, and find missing dimensions while improving accuracy with multi-step 3D shape problems.
For students who know length × width × height, but need practice applying it to more complex 3D shapes.
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What Do Compound Cuboid Volume Questions Look Like?
Students are given 3D composite shapes made from rectangular prisms and must find the total volume or an unknown side length. Questions often involve splitting stacked blocks or subtracting a missing cut-out section to calculate the correct measurement. Here is a worked example.
Add Two Stacked Cuboids
Question: A 4 cm × 2 cm × 4 cm cuboid sits on a 9 cm × 2 cm × 4 cm cuboid. What is the total volume?
Worked Method
Step 1: Bottom cuboid = 9 × 2 × 4 = 72 cm³.
Step 2: Top cuboid = 4 × 2 × 4 = 32 cm³.
Step 3: Total volume = 72 + 32 = 104 cm³.
Tip: Split a stacked shape into separate cuboids and add their volumes. Do not count an overlapping region twice.
Rules to Help You Solve Compound Cuboid Volume Questions
As shown in the example above, breaking a compound 3D solid into simple rectangular blocks makes finding total volume straightforward. Use these core rules to approach stacked shapes, cut-outs, and missing measurements systematically.
📦 Rule 1: Volume = length × width × height
Calculate each rectangular block separately before combining the results.
Example: A 9 cm × 2 cm × 4 cm block has volume 72 cm³.
➕ Rule 2: Split stacked solids into blocks
For a stepped or stacked shape, add the volume of each non-overlapping cuboid.
Example: 32 cm³ + 72 cm³ = 104 cm³.
➖ Rule 3: Subtract a cut-out cuboid
When a corner is removed, calculate the full outer cuboid and subtract the missing block.
Example: 140 cm³ − 24 cm³ = 116 cm³.
↩ Rule 4: Work backwards for missing lengths
For a missing cut-out height, find the removed volume and divide by the cut-out's width × depth. For an unknown shared depth, divide the remaining solid's volume by its remaining front-face area.
Example: 72 cm³ ÷ 36 cm² = 2 cm.
Two More Worked Examples
Practise finding volume by subtracting a cut-out corner, then learn how to work backwards from a known volume to find a missing height.
Subtract a Corner Cut-Out
Question: A cuboid is 7 cm wide, 5 cm high, and 4 cm deep. A corner is removed through its full depth, leaving an upper ledge 4 cm wide. The cut-out is 2 cm high. What volume remains?
Worked Method
Step 1: Full cuboid = 7 × 5 × 4 = 140 cm³.
Step 2: Cut-out width = total width − upper ledge width = 7 − 4 = 3 cm.
Step 3: Cut-out cuboid = 3 × 2 × 4 = 24 cm³.
Step 4: Remaining volume = 140 − 24 = 116 cm³.
Tip: Subtraction works well when the shape is easiest to see as one complete cuboid with a corner missing.
Work Backwards to Find a Missing Length
Question: A cuboid is 10 cm wide, 7 cm high, and 6 cm deep. A corner is removed through its full depth, leaving an upper ledge 4 cm wide. The remaining volume is 348 cm³. Find the cut-out's missing height, x.
Worked Method
Step 1: Full cuboid = 10 × 7 × 6 = 420 cm³.
Step 2: Cut-out volume = 420 − 348 = 72 cm³.
Step 3: Cut-out width = total width − upper ledge width = 10 − 4 = 6 cm.
Step 4: Cut-out base area = width × depth = 6 × 6 = 36 cm².
Step 5: Divide the removed volume by its base area: x = 72 ÷ 36 = 2 cm.
Answer: x = 2 cm.
Tip: Use the removed 72 cm³ when finding the cut-out height. Dividing the remaining 348 cm³ by the cut-out base area mixes measurements from different solids.
