Composite Prism Volume
A composite prism is made by joining simpler prism parts. To find its volume, break the solid into familiar pieces, find each piece’s volume, then add the results.
1) Split the figure
- Identify the separate prism parts.
- If a shape is missing from a larger prism, treat it as a “cut-out” and subtract its volume.
- Keep track of matching dimensions so you do not count any part twice.
2) Find each prism’s volume
Use the prism volume idea: volume = base area × height.
- First find the area of each base.
- Then multiply by the prism’s length or height, depending on the drawing.
- Write units as cubic units.
3) Add or subtract carefully
- Add volumes for pieces that are joined together.
- Subtract volumes for removed sections.
- Simplify the final expression or number completely.
4) Check your work
- Make sure every dimension was used in the correct place.
- Confirm the final answer is in cubic units.
- A quick sanity check: the composite volume should be reasonable compared with the size of the figure.
If the solid can be separated in more than one way, choose the method that gives the cleanest calculations and the simplest exact answer.