Volume is the amount of space a three-dimensional object takes up. We measure volume in cubic units.
Volume is different from area. Area measures flat surfaces (two dimensions), while volume measures space (three dimensions).
To find the volume of a rectangular prism, multiply its length × width × height.
Volume = length × width × height
V = l × w × h
A box is 5 cm long, 3 cm wide, and 2 cm high.
Volume = 5 × 3 × 2 = 30 cubic centimeters (cm³)
All measurements must be in the same units before multiplying. The answer will be in cubic units.
We can find volume by counting how many unit cubes fit inside a solid shape.
Imagine a rectangular prism that is 4 cubes long, 3 cubes wide, and 2 cubes high.
To find the total cubes:
Volume = 24 cubic units
This method helps you understand why we multiply length × width × height to find volume.
Composite figures are made by putting together two or more rectangular prisms.
An L-shaped bookshelf can be divided into two rectangular prisms:
When breaking apart composite figures, make sure you don't miss any parts or count any parts twice.
We use volume to solve everyday problems involving space and capacity.
A moving box measures 2 feet by 1.5 feet by 1 foot. What is its volume?
Volume = 2 × 1.5 × 1 = 3 cubic feet
Always read word problems carefully to identify the measurements you need. Draw a picture if it helps!