# Finding the Volume of a Rectangular Prism

Instructor: Thomas Higginbotham

Tom has taught math / science at secondary & post-secondary, and a K-12 school administrator. He has a B.S. in Biology and a PhD in Curriculum & Instruction.

Many shapes in our world, such as cereal boxes and bricks, are rectangular prisms. Often, we have to know how much volume a rectangular prism takes up. In this lesson, learn how to calculate the volume of a rectangular prism.

## Let's Fill a Box with Honey

Your friend cheated on a bet, but you're person of your word, so now you owe him 25 dollars. How funny, you think, would it be to send it to him in pennies? And you know what would be even funnier? A box filled to the top with honey! Cackling, you head to the grocery store and quickly realize you don't know how much honey to buy.

You might now reflect on why it would have been wise to pay attention in math class (so you can make life difficult for your friend, of course!) but not to worry. This lesson will help you not only pick on your friend, but also learn a little bit about finding the volume of rectangular prism.

## What a Prism Is

A prism is a geometric shape that has parallel ends that are the same shape and size, as well as sides that are parallelograms. That's the technical definition, though it's probably easier to explain what a prism is by explaining what a prism is not.

A cylinder is really close to being a prism, though it is not one. It has the parallel, same shape ends, but it does not have parallelogram sides. It has curved sides, as seen in the first picture. The picture also shows two other images that are not prisms because they don't follow our prism rules.

So what is a prism? Imagine a cylinder of clay standing on its end. If you take a straight edge knife and cut from the top of the cylinder vertically down to the bottom, you can create a flat side. Then, by continuing to make cuts until all of the round parts are gone, you will have a prism once all of the rounded parts of the sides are gone.

It doesn't matter how many cuts you make, as long as they're straight down from the top to the bottom. They could be six similar cuts making a perfect hexagonal prism shape, or they could be 17 cuts, making a different kind of prism.

Another way to think about a prism is a shape that has the same cross-section (a cut made parallel to the same size and shaped ends), no matter where you make the cut.

## What a Rectangular Prism Is

A rectangular prism is simply a prism that has every side connected with every other side by a 90-degree angle. In other words, something like a rectangular box or a cube.

Common objects that are rectangular prisms are cereal boxes, six-sided dice, and many aquariums.

## Finding the Volume of a Rectangular Prism

The great thing about finding the volume of a rectangular prism is that it is one of the easiest calculations there is. However, before getting to that, it might be helpful to go back to the basics of why this calculation is so easy. Let's think about two rectangular prisms, like the ones we have below.

The first one is 1 inch wide 1 inch tall and 8 inches long. The second one is 2 inches wide 4 inches long and 1 inch high. It's pretty easy to visualize how many 1 inch cubes (a rectangular prism with each side measuring 1 inch) would fit into these rectangular prisms. For each, 8 cubes fit in.

This is the volume of each prism, 8 cubic inches. Mathematically, we could have calculated this by simply multiplying each of the sides together. In the first example, 1 times 1 times 8 equals 8. In the second example, 2 times 4 times 1 also equals 8. The easy formula to find the volume of a rectangular prism? Volume equals length times width times height, or:

V = L x W x H

It's just that simple! In the real world, volume of rectangular prisms is not usually as easy to calculate, since their sides are not always whole numbers like in the most recent example, but the formula always works.

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