Volume of a rectangular prism. How to calculate the volumes cuboids (or boxes).
Volume Of A Cuboid Video
The volume of a rectangular prism (or cuboid) has one of the easiest formulas out of all of the 3D shapes. All you need to do is multiply all 3 side lengths together. Therefore, the formula for the volume of a rectangular prism is:
Volume = height × length × width
Or
V = hlw if you prefer a more algebraic version.
It doesn’t matter what order you multiply the side lengths together as you will always get the same answer. So don’t worry about deciding which side is the length, width or height – just multiply the 3 side lengths of the rectangular prism together.
Example 1
Work out the volume of this rectangular prism.
So all you need to do is to multiply the three side lengths together. Remember that is doesn’t matter which order you multiply the three numbers in as you will get the same answer.
4 × 3 × 20 = 240 cubic feet.
Or if you prefer you could lay it out in a more formal approach by applying the formula V = hlw:
V = hlw
= 4 × 20 × 3
= 240 cubic feet
Example 2
Work out the volume of this rectangular prism.
Just like example 1 all you need to do is to multiply the three side lengths together. Remember that is doesn’t matter which order you multiply the three numbers in as you will get the same answer.
6 × 3 × 14 = 252 m³.
Or if you prefer you could lay it out in a more formal approach by applying the formula V = hlw:
V = hlw
= 14 × 3 × 6
= 252 m³
Example 3
A small red rectangular prism has dimensions 3 by 2 by 4. A larger blue rectangular prism has dimensions of 15 by 6 by 32. Work out how many of the red rectangular prism fit into the blue rectangular prism.
In order to do this you will need to work out the volumes of both prisms.
Volume of red rectangular prism = 3 × 2 × 4 = 24 cm³
Volume of blue rectangular prism = 15 × 6 × 32 = 2880 cm³
Now if you divide the two volumes then this will tell you how many of the small rectangular prisms fit into the larger rectangular prism:
2880 ÷ 24 = 120
So 120 red boxes will fit into the large rectangular prism.
