Volume of Right Prisms
Warmup
Select all the prisms.
Activity #1
Use snap cubes to build a 3-D Shape.
In the applet below, you can keep dragging blocks out of the pile by their red points until you have enough to build what you want.
- Use the snap cubes to build the shape you see on the paper. (You can keep dragging blocks out of the pile by their red points until you have enough to build what you want.)
- Answer question 1 below.
- Add another layer of cubes on top of the shape you have built.
- Now answer the rest of the questions below.
(1.) Using the face of a snap cube as your area unit, what is the area of the shape? Explain or show your reasoning using the applet below.
(2.) Describe this three-dimensional object.
(3.) What is the volume of your object? Explain your reasoning.
(4.) Right now, your object has a height of 2. What would the volume be if it had a height of 5?
(5.) Right now, your object has a height of 2. What would the volume be if it had a height of 8.5?
Activity #2
The applet below has a set of three-dimensional figures. Note that each polyhedron has only one label per unique face. Where no measurements are shown, the faces are identical copies.
- The first one has already been choosen.
- Rotate the view using the Rotate 3D Graphics tool marked by two intersecting, curved arrows. If you do not see it click on the 3D Graphics window for the full toolbar to appear.
- Use the distance tool to click on any segment to find the height or length.
- Then fill in the required information in the table below.
- Choose another figure using the slider and repeat all the steps above.
Activity #3
Explore Features of Polyhedra.
There are 4 different prisms that all have the same volume. Here below is what the base of each prism looks like.
- Order the prisms from shortest to tallest.
(1.) Explain your reasoning.
(2.) If the volume of each prism is 60 cubic units, what would be the height of each prism?
(3.) For a volume other than 60 cubic units, what could be the height of each prism?
Challenge #1
For each prism, shade one of its bases.
Challenge #2
The volume of both of these trapezoidal prisms is 24 cubic units. Their heights are 6 and 8 units, as labeled.
What is the area of a trapezoidal base of each prism?
Quiz Time