🧊 Volume of Composite Shapes

What you’ll learn

1. Volume Is the Space InsideDefine volume as the amount of 3D space inside a solid, measured by counting unit cubes.Volume answers how much space fills a solid and is measured in cubic units. It is fundamentally a count of unit cubes — cubes one unit long on every side — that pack inside the object.
2. The Volume of a Single BoxFind the volume of a rectangular prism using length × width × height.The bottom layer of a box holds length × width cubes, and stacking it height times gives length × width × height. This single formula, worked as 6 × 3 × 2 = 36 cm³, is the only one the course requires.
3. Two Boxes Stuck TogetherDecompose an L-shaped composite solid into two rectangular prisms and add their volumes.A composite solid such as an L is simply two boxes joined. Splitting it, finding each box's volume with l × w × h, and adding — 36 + 24 = 60 cm³ — gives the whole volume without any new formula.
4. More Than One Way to SliceRecognise that different valid decompositions of the same solid give the same volume.A solid can be split in more than one place, and every correct split yields the same total volume because the enclosed space is unchanged. Learners choose the decomposition with the friendliest numbers.
5. Finding a Missing LengthDeduce an unlabelled dimension by subtracting a known part from an overall measurement.Real problems often omit a length. Because stacked parts add up to the overall size, a missing dimension is the whole minus the known piece — for example, a 6 cm total minus a 2 cm base gives a 4 cm upright.
6. The Take-Away TrickFind a composite volume by enclosing the solid in a full box and subtracting the missing chunk.An alternative to split-and-add is to fill the solid to a complete box, compute that volume, and subtract the empty chunk: 108 − 48 = 60 cm³. Both methods agree, so each can check the other.
7. Putting It All TogetherApply the full four-step method and use estimation to check a composite-volume answer.The routine is: split into boxes, find missing lengths by subtracting, compute each volume with l × w × h, then add (or subtract the gap). Estimating with the enclosing box first provides a safety net against large errors.

Questions this course answers

Grounded in trusted sources

• Khan Academy — Volume of composite figures (rectangular prisms)
• BBC Bitesize — Volume of cuboids and compound solids (KS2/KS3)
• Common Core State Standards — 5.MD.C.5c (volume of figures composed of two right rectangular prisms)

Every Wunder lesson is built from real, reputable sources — never invented.

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