Video:How to Find the Volume and Surface Area of a Rectangular Prismwith Eric Stone
Our expert teaches you how to calculate the volume and surface area of a rectangular prism. See these helpful tips for easily finding the volume and surface area of a rectangular prism.See Transcript
Transcript:How to Find the Volume and Surface Area of a Rectangular Prism
Hi, I am Eric Stone from South Burlington High School in South Burlington, Vermont, here for About.com. Today, we are going to talk about the surface area and volume of a rectangular prism.
Definition of a Rectangular Prism
Now a rectangular prism is just what everyone normally thinks of as a box -- a three dimensional box. It has a length, it has a width, and it has a height: length times width times height. It really doesn't matter which you call the length, which you call the width or which thing you call the height, as long as you understand that the length and the width and the height are the three cardinal directions.
Finding the Volume of a Rectangular Prism
Let's start by finding the total volume. The volume, like almost any geometric figure, is found by taking the area of the base and then multiplying by its total height as it moves through space. Now for a rectangular prism, the area of the base is a constant, it's a rectangle. Any slice you take at any point along the surface, that slice will be a rectangle. So, finding the volume is merely taking the base and multiplying it by the height -- no funny business required! So the volume is nothing more than the length times the width times the height.
Finding the Surface Area of a Rectangular Prism
To find the surface area, it's a little more complicated. What you have to do is you have to understand that for a rectangular prism there are six different sides that you need to find the area of. Then all you have to do is add them all together. So on a rectangular prism or a box, you have one side which is a rectangle, but there's one exactly like it on the other side of the prism. So you have two of those. Then you have this piece right here -- that's a rectangle, too. I need to find the area of that rectangle, but you have to understand there's one on the other side just like it. So there's two of those. And then last, but not least, there's this rectangle on the top. You want to find the area of that rectangle, too. But there's another one just like it on the other side of the box.
See where the trend is? You have one side -- there's two of them. Another side -- there's two of them. And there's two of the other side, for a total of six sides. So, these are the three different rectangles you need to think about. You have the piece that was on the top, and the area of that is nothing more than the width times the height. You have the pieces on the side, and the area of those are nothing more than the length times the width. And you have the piece that goes up and down, which is nothing more than the length times the height.
Basic Formula for Finding the Volume and Surface Area of a Rectangular Prism
So, long story short, if you want to find the total area, you just have to take two of each. So it's going to be two width times height, plus two length times width, plus two length times heights. So in other words, if you just take each of the dimensions, the length, the width, and the height, and multiply them each by each other and multiply each of those by two, you're good to go!
Your formula for the surface area of a rectangular prism: A = 2wh + 2lw + 2lh.
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