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
Intermediate (3-5)
Lesson Type
Quick Query

Lesson Plan - Get It!

Audio:

Desmond works for a new construction company specializing in building homes, offices, and restaurants from shipping containers.

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

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

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

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

Sketch this tiny coffee shop.

The volume is all the space that fills the inside of this solid figure. To find the volume of a rectangular prism, use this formula.

Volume = Length x Width x Height

Now, 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 you 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, sketch the building.

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

To find the total volume of the figure, first, you need to calculate the volume for figure A.

Next, find the volume for Figure B.

• But how do you know the width of Figure B?

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

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

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

Now, 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!

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