Unit 7, Lesson 12
Volume of Right Prisms
Grade 7
Preparation
Lesson Narrative
In this lesson, students learn that they can calculate the volume of any right prism by multiplying the area of the base by the height of the prism. Students make sense of this formula by picturing the prism decomposed into identical layers, each 1 unit tall. These layers are composed of a number of cubic units equal to the number of square units in the area of the base. The height of the prism tells how many of these layers there are. Therefore, multiplying the number of cubic units in one layer by the number of layers gives the total number of cubic units in the prism, regardless of the shape of the base.
Students construct and critique arguments about whether or not some three-dimensional figures are prisms (MP3). They then decide whether they can apply the formula to calculate the volume. If so, they identify the base and measure the height, and they then calculate the volume. In the optional activity, students apply the formula to find the height of a prism, given its volume and the area of its base.
- Determine the volume of a right prism by counting how many unit cubes it takes to build one layer and then multiplying by the number of layers.
- Generalize (orally) the relationship between the volume of a prism, the area of its base, and its height.
- Identify whether a given figure is a prism, and if so, identify its base and height.
Let’s look at volumes of prisms.
Required Preparation
You will use only one of the two pages of the blackline master. If your snap cubes measure inch, print the first page of the blackline master, with the slightly smaller shapes. If your snap cubes measure 2 cm, print the second page of the blackline master, with the slightly larger shapes. Make sure to print the blackline master at 100% scale so that the dimensions are accurate. Prepare 1 copy for every 6 students, and cut the pages in half so that each group of 3 students has one half-page.
For the digital version of the activity, acquire devices that can run the applet.
Print, cut, and assemble the nets from the blackline master. Card stock paper is recommended. Make sure to print the blackline master at 100% scale so the dimensions are accurate. Prepare 1 polyhedron for every 3 students (1 copy of the entire file for every 18 students).
For the digital version of the activity, acquire devices that can run the applet.
Volume is the number of cubic units that fill a three-dimensional region with no gaps or overlaps.
This rectangular prism has 3 layers that are each 20 units3. So, the volume of the prism is 60 units3.