You can find volumes of single and combined prisms. In word problems you also work backward to a missing edge, compare containers, and decide which unit makes sense.
Key idea
Use $V = l \times w \times h$ forward to find a volume, or backward to find a missing edge: divide the volume by the area of the base. Give volumes in cubic units.
Why it works
If a box holds 120 cubes and its base is $6 \times 4 = 24$ cubes, then the number of layers is $120 \div 24 = 5$. Dividing undoes multiplying. Units tell you what you measured: square units for a flat surface, cubic units for the space inside.
Worked examples
Worked example: A missing edge
A box has a volume of 120 cubic inches. It is 6 inches long and 4 inches wide. How tall is it?
- Base area: $6 \times 4 = 24$ square inches.
- Height: $120 \div 24 = 5$.
- Check: $6 \times 4 \times 5 = 120$.
Answer: 5 inches
Worked example: Compare two boxes
Box A is 5 in by 4 in by 3 in. Box B is 6 in by 3 in by 3 in. Which holds more, and by how much?
- A: $5 \times 4 \times 3 = 60$ cubic inches.
- B: $6 \times 3 \times 3 = 54$ cubic inches.
- $60 - 54 = 6$.
Answer: Box A, by 6 cubic inches
Worked example: Bigger cubes
How many 2-cm cubes fit in a box 6 cm by 4 cm by 4 cm?
- Along each edge: $6 \div 2 = 3$, $4 \div 2 = 2$, $4 \div 2 = 2$.
- $3 \times 2 \times 2 = 12$ cubes.
Answer: 12 cubes
Common mistake
Giving square units for a box's capacity, such as “45,000 square centimeters” for a fish tank. Capacity is the space inside, so it is counted in cubes. Check the unit: three lengths multiplied give cubic units.