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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The Rules Every Compound Cuboid Volume Question Uses
These papers test the same core cuboid formula in different forms: stacked blocks, cut-out solids, decimals, and missing measurements. A clear diagram plan keeps the arithmetic manageable.
📦 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
Find the missing block's volume, then divide by its known width × depth area.
Example: 72 cm³ ÷ 36 cm² = 2 cm.
3 Worked Compound Cuboid Volume Examples
Start by adding stacked cuboids, then handle a corner cut-out, and finally work backwards to find a missing length.
1. 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.
2. Subtract a Corner Cut-Out
Question: A solid starts as a 7 cm × 5 cm × 4 cm cuboid. A 3 cm × 2 cm × 4 cm corner is removed. 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.
3. Work Backwards to Find a Missing Length
Question: A 10 cm × 7 cm × 6 cm cuboid has a corner cut out. The remaining volume is 348 cm³. The cut-out is 6 cm wide and 6 cm deep. Find its 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: Known cut-out area = 6 × 6 = 36 cm².
Tip: Divide volume by area: x = 72 ÷ 36 = 2 cm. The common mistake is dividing the remaining 348 cm³ instead of the removed 72 cm³.
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 Compound Cuboid Volume pack contains 90 questions across 3 printable test sets. Students practise cuboid volume, stacked solids, cut-out shapes, decimal measurements, and missing dimensions.
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