You can find the volume of a rectangular prism. Many solids, like steps or an L-shaped building, are two or more prisms joined together.
Key idea
Split the solid into rectangular prisms that do not overlap. Find each volume and add. Volume is additive: the whole holds as many cubes as its parts together.
Why it works
Every unit cube in the solid belongs to exactly one of the parts, so adding the parts counts each cube once. If the parts overlapped, the shared cubes would be counted twice, which is why the split must have no overlap. Sometimes you need to find a missing measure by subtracting, such as the height of the bottom part.
Worked examples
Worked example: Two stacked prisms
Find the volume of the step shape above.
- Bottom: $6 \times 3 \times 2 = 36$ cubic cm.
- Top: $3 \times 3 \times 3 = 27$ cubic cm.
- Total: $36 + 27 = 63$ cubic cm.
Answer: 63 cubic centimeters
Worked example: Find a missing height first
A solid is 5 m tall. Its top part is a $2 \times 4 \times 3$ prism (3 m tall), sitting on a bottom part that is 6 m long and 4 m wide. Find the volume.
- The bottom part's height is $5 - 3 = 2$ m.
- Bottom: $6 \times 4 \times 2 = 48$. Top: $2 \times 4 \times 3 = 24$.
- Total: $48 + 24 = 72$.
Answer: 72 cubic meters
Common mistake
Counting a shared part twice, such as using the full height of 5 m for the bottom prism in the second example. Then the top part's cubes are counted again. Check: make sure no cube belongs to both parts. The heights of the stacked parts must add to the whole height.