Volume of Composite Rectangular Prisms

Lesson Plan - Get It!

Audio:

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.

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

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.

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

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.

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.

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

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!