Volume of Composite Rectangular Prisms

Contributor: Ashley Nail. Lesson ID: 13890

You know how to find the volume of a rectangular prism. But do you know how to find the total volume of a figure made up of more than one rectangular prism?

categories

Measurement and Data

subject
Math
learning style
Visual
personality style
Lion, Otter, Beaver, Golden Retriever
Grade Level
Intermediate (3-5)
Lesson Type
Quick Query

Lesson Plan - Get It!

Audio:

Desmond works for a new construction company whose specialty is building homes, offices, and restaurants out of shipping containers.

Look at one of the restaurants Desmond made out of a shipping container:

restaurant

Desmond is currently working on an office and needs to figure out which air conditioner will most efficiently circulate cool air throughout the whole building.

office

To find the best air conditioner, Desmond needs to calculate the total volume of the space.

Let’s look at a few of Desmond’s other buildings to practice finding the volume.

building 1

Let’s draw a sketch of this tiny coffee shop.

sketch of building 1

The volume is all the space that fills the inside of this solid figure. In order to find the volume of a rectangular prism, we will use this formula:

Volume = Length x Width x Height

Now, let’s use the formula to find the volume of the container coffee shop.

V = L x W x H

V = 16 x 8 x 10

V = 1,280

V = 1,280 cubic feet

Most of Desmond’s buildings use more than one shipping container pieced together, like the office.

  • How can we find the volume of more complicated buildings?

You can find the volume as long as the total figure can be decomposed into smaller rectangular prisms.

For example, look at another of Desmond’s buildings.

building 2

Now, let’s draw a sketch of the building.

building 2 sketch

Notice that the total figure has been decomposed into two different rectangular prisms, named A and B.

In order to find the total volume of the figure, first we need to calculate the volume for figure A.

figure A

Next, let’s find the volume for figure B.

  • But how do we know the width of figure B?

Notice that figure A and figure B both share the same measurement for length.

figure B

Now, to find the total volume for the entire figure, we’ll add the volumes of each rectangular prism.

total volume

Desmond’s building has a total volume of 5,984 cubic feet.

Now, let’s practice finding the total volume of a solid figure by decomposing rectangular prisms.

Click NEXT to visit the Got It? section to try finding total volume on your own!

Elephango's Philosophy

We help prepare learners for a future that cannot yet be defined. They must be ready for change, willing to learn and able to think critically. Elephango is designed to create lifelong learners who are ready for that rapidly changing future.