Embedded Files
Learning Targets
I can explain why the volume of a prism can be found by multiplying the area of the base and the height of the prism.
Notes
Notes
Here are some right prisms. There are many more types. Prisms are three-dimensional figures who have rectangles as the sides of the shape but any polygon as the bases.
When we slice a three-dimensional object, we expose new faces that are two dimensional. The two-dimensional face is a cross section. Many different cross sections are possible when slicing the same three-dimensional object.
Here are two peppers. One is sliced horizontally, and the other is sliced vertically, producing different cross sections.
The imprints of the slices represent the two-dimensional faces created by each slice.
It takes practice imagining what the cross section of a three-dimensional object will be for different slices. It helps to experiment and see for yourself what happens!
Any cross section of a prism that is parallel to the base will be identical to the base. This means we can slice prisms up to help find their volume. The volume of a three-dimensional figure is a measure of the amount of space that it occupies. Volume is measured in cubic units. For example, if we have a rectangular prism that is 3 units tall and has a base that is 4 units by 5 units, we can think of this as 3 layers, where each layer has 4 • 5 cubic units.
That means the volume of the original rectangular prism is 3(4 • 5) cubic units.
This works with any prism! If we have a prism with height 3 cm that has a base of area 20 cm2, then the volume is 3 • 20 cm3 regardless of the shape of the base. In general, the volume of a prism with height h and area B is
V = B • h
For example, these two prisms both have a volume of 100 cm3.
Formula
Formula
The volume V of a prism is the product of the area of the base and the height of the prism.
Vocabulary
Vocabulary
cross section
A cross section is the new face you see when you slice through a three-dimensional figure.
For example, if you slice a rectangular pyramid parallel to the base, you get a smaller rectangle as the cross section.
Activities
Activities
12.2 Finding Volume with Cubes
12.2 Finding Volume with Cubes
This applet has 64 snap cubes, all sitting in the same spot on the screen, like a hidden stack of blocks. You will always know where the stack is because it sits on a gray square. You can keep dragging blocks out of the pile by their red points until you have enough to build what you want.
Click on the red points to change from left/right movement to up/down movement.
There is also a shape on the grid. It marks the footprint of the shapes you will be building.
Using the face of a snap cube as your area unit, what is the area of the shape? Explain or show your reasoning.
Use snap cubes to build the shape from the paper. Add another layer of cubes on top of the shape you have built. Describe this three-dimensional object.
What is the volume of your object? Explain your reasoning.
Right now, your object has a height of 2. What would the volume be
if it had a height of 5?
if it had a height of 8.5?
Add to Your Notes
Add to Your Notes
Calculating the total number of cubes to make a prism is the same thing as calculating the volume of the prism!
We can find the area of the base of the prism and multiply by the number of layers (height) of the prism!
height of the prism is measured in units
area of the base is measured in units2
volume of the prism is measured in units3
Mrs. Huntings Activity - Can You Find the Volume?
Mrs. Huntings Activity - Can You Find the Volume?
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Assignment
Assignment
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