Volume of Rectangular Prisms Educational Resources K12 Learning, Geometry, Measurement and Data, Math Lesson Plans, Activities, Experiments, Homeschool Help

Lesson Plan - Get It!

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Imagine making a batch of delicious chocolate fudge to share with your family and friends. You cut your finished fudge into 1 inch cubes. You find the perfect red box. This will be a great way to gift your fudge to your family!

But how much fudge will fit inside the box?

You will need to find the volume of the box in order to answer that question!

Before we figure out how much fudge can fit inside your box, let's review a few concepts you've already learned about shapes.

First, a box is a solid shape. It is a rectangular prism. For more information, review the Related Lesson on shapes found in the right-hand sidebar.

A rectangular prism is three-dimensional and has a base with width and length measurements. The shape also has a height measurement.

rectangular prism

Second, we will be finding the volume of a shape in this lesson. Volume is related to the area, surface area, and perimeter.

For more information, review the Related Lessons found in the right-hand sidebar.

Perimeter finds the measurement around a plane shape. Area finds the measurement of the space covering a plane shape. Volume finds the measurement of the amount it takes to fill a solid shape.

In order to figure out how much fudge to make, we need to be able to measure the space inside of our box. This measurement is called volume.

We measure volume in cubic units. This is a unit cube:

cubic unit

So, we find the volume by figuring out how many of these cubic units fit inside of a rectangular prism.

For example, look at this rectangular prism:

example 1

We can start filling in the rectangular prism with cubic units:

example 2

How many cubic units will fill the base layer of the shape?

If you thought 28, you are correct! We know it is 28 cubic units because we are basically making an array using the length and width of 7 and 4.

We are also finding the area of the base:

example 3

We can fit four layers of 28 inside of our rectangular prism. We know this because the height of our shape is 4 cubic units.

28 + 28 + 28 + 28 = 112

We can fit 112 cubic units inside of the rectangular prism! The volume is 112 cubic units!

We can also find the volume of a rectangular prism by using a formula:

Volume = Width x Height x Length

V = W x H x L

Let's look at the rectangular prism again and this time use the formula to find volume!

example 4

Now you are ready to practice finding the volume of rectangular prisms! You can figure out the volume of our box and find how much fudge we need to make!