SME
Grade 5 Math · Measurement & Data
Volume of rectangular prisms (length × width × height)
Use this for “A box is 4 cm long, 3 cm wide and 2 cm tall. What is its volume?”
Diagram
The shaded bottom layer is 4 × 3 = 12 cubes.
2 layers: 12 × 2 = 24 cubes.
This is an example. Type your own values to start a new problem.
Length (cm)
×
Width (cm)
×
Height (cm)
=
Volume (cm³)
Base area
worked out (not typed)
Formulas
4 × 3 = 12
Length × width = base area
12 × 2 = 24
Base area × height = volume
Assumptions
•
Volume counts the unit cubes that fill the box.
•
The base area is length × width: the cubes in one layer. The box has a layer for every unit of height.
•
Volume = length × width × height, in cubic units. Sides to 100 (40 × 60 × 80 cm).
•
Give the volume and two sides to find the missing side.
•
Past 10 a side, the box is drawn to scale with one unit cube beside it.
Step-by-step
WE KNOW
Length: 4 cm
Width: 3 cm
Height: 2 cm
FIND
base area, volume
Step 1 · Find base area
4 × 3 = ?
Length × width = base area
The base area: rows of cubes along the length, one row for each unit of width.
Base area = 12 cm²
Step 2 · Find volume
12 × 2 = ?
Base area × height = volume
A layer for every unit of height: multiply the base area by the height.
Volume = 24 cm³
Check
Put the numbers back in. Both sides should match.
4 × 3 = 12 ✓
12 × 2 = 24 ✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.