Volume of Rectangular Prisms

Objective: To develop and use a formula for the volume of a rectangular prism

What is volume?

 The volume of a solid object such as a brick or a ball is a measure of how much space the object takes up. The volume of a container such as a box is a measure of how much the container will hold.

How do we measure volume?

 Volume is measured in cubic units. (cubic inches, cubic feet, etc.)  We said a square unit is a measure with two sides being a related unit of length.

1 unit 1 unit

How do we measure volume?

 Volume is measured in cubic units. (cubic inches, cubic feet, etc.)  A cubed unit of measure is a measure with three sides being a related unit of length. The third side comes off the paper into the 3-dimensional plane 1 unit 1 unit

How do we measure volume?

 Cubed units can be written in a variety of ways:    inches cubed inches³ in.³ 1 unit 1 unit

Finding Volume of a Rectangular Prism  To find the volume of a rectangular prism, all you need to know are the length and width of its base and its height.

 These are called the dimensions of the prism.

length width

Finding Volume of a Rectangular Prism  To find the volume using these dimensions, multiply the length x width (6 x 7 = 42 feet)  This represents one layer (or one foot). Now multiply this surface area by the number of layers (or height) 6 feet

42 x 8 = 336 feet³

7 feet

Math Journal page 328

 Work through page 328  You will need to use Activity sheet 7 which is located in the back of your math journal.

 Please follow the directions and

do not

tear out the page or cut our the shapes.

Let’s talk about it.

Now you can cut!

    Remove Activity Sheet 7 from the back of your journal.

Cut out the pattern for Box A (only) along the outside edges.

Fold it on the dashed lined and tape it to make an open box.

Bring your box to a teacher. In order to advance to the next level, you need to collect 24 centimeter cubes.

Now you can cut!

  Bring your box to a teacher. In order to advance to the next level, you need to collect 24 centimeter cubes.

In order to get the cubes, you will need to identify the following parts of the box:

base height faces edges vertices

How many?

    How many centimeter cubes cover the bottom of the box?

8 cubes Add a second layer. How many total cubes are in the box now?

16 cubes Add a third layer. How many cubes are in the box? 24 cubes What is the volume of the box if measured in cubic centimeters? Think about how you would write that.

24 centimeters ³ 24 cm. ³

On to Box B

 Cut out Box B  Use the grid to make a prediction of the volume.

 Next, fill the base with centimeter cubes to find the surface area of one layer.

 Using that information, determine the area based on the number of layers.

 Use the blocks to prove your answer. You will need to share blocks with your neighbor.

And Box B contains….

45 cm³

Open your Math Journal to page 329 Complete pages 329 and 330 with a partner.

Show your completed work to a teacher to receive your homework assignment .