Definition: The volume of a rectangular prism is the product of its length, width, and height, V = lwh, measured in cubic units.
What is volume?
Volume is the amount of space inside a solid. We count how many unit cubes fit, so the units are cubic, like cubic inches.
What is the formula?
For a rectangular prism, V = l x w x h. Equivalently, V = B x h, where B is the area of the base.
How do you apply it?
Mathbot builds a toolbox 14 inches long, 6 inches wide, and 5 inches tall.
- Base area: 14 x 6 = 84 square inches.
- Multiply by height: 84 x 5 = 420.
The volume is 420 cubic inches.
Can sides be fractions?
Yes. A prism with sides 2 1/2, 4, and 1 1/2 units has volume 5/2 x 4 x 3/2 = 60/4 = 15 cubic units. Counting 1/2-unit cubes gives the same result.
What is the common error?
Mixing up units or adding the dimensions. Adding 14 + 6 + 5 gives 25, which has no relation to volume. Multiply. Also, make sure all edges use the same unit before you multiply.