Finding the volume of a rectangular prism is pretty straightforward. You simply multiply the length, the width, and the height. Sometimes, though, one of the dimensions is called depth.
Volume of a Rectangular Prism
V = l × w × h
The tabs below show this formula in action.
Problem 1
Problem 2
Problem 3
How would you find the volume of this rectangular prism?
Let's use the volume formula for a rectangular prism.
V = l × w × h
V = 4 units × 2 units × 3 units = 24 cubic units
This refrigerator is 72 inches tall, 36 inches wide, and 24 inches deep. How many cubic inches can this refrigerator hold?
We need to calculate the volume of this refrigerator.
V = l × w × h
V = 72 in × 36 in × 24 in
V = 62,208 in3
In the real world, refrigerator capacity is usually given in cubic feet, not cubic inches. What is the volume in cubic feet?
There are a couple of ways to do this problem. We'll do it by converting our inches to feet and redoing the volume calculation.
72 in → 6 ft
36 in → 3 ft
24 in → 2 ft
V = 6 ft × 3 ft × 2 ft = 36 ft3
If you are good at dimensional analysis, you can convert the 62,208 in3 to cubic feet directly, but that's for another lesson.
Here we have an oblique rectangular prism. Basically, it's a rectangular prism that's been pushed over a bit.
Don't let the slant height of 5 units fool you. That is NOT the height that goes into the volume formula. The height that we use is 3 units. We need the height that is perpendicular (straight up) to the base, not the height that is at a slant angle with the base. Sometimes you may have to use some triangle calculations (like the Pythagorean theorem or trigonometry ratios) to calculate that height.
So what's the volume?
V = 4 units × 2 units × 3 units = 24 cubic units
