50 POINTS FOR THIS PLEASE HELP!
PROJECT: SOLID FIGURES
In this chapter, we have looked at rectangular prisms in two ways: either drawn to show the three-dimensional shape, or drawn as a net to show all the two-dimensional surfaces:
img/img_threed_and_twod_prism.gif
However, there is another way to show the two-dimensional views of a three-dimensional prism, called orthographic projection.
img/img_orthographic_views.gif
These views show what the prism looks like if we view it from the front, top, and side.
In this project, you will build and draw two-dimensional views of solid figures, and use them to find the surface area of the figure.
OBJECTIVES
Construct solid figures using blocks or sugar cubes.
Draw 2-d views of these figures.
Find surface area and volume of rectangular prisms.
Materials
Pencil
Grid paper
Straight edge
Blocks or sugar cubes
In this project, you will build your own 3D figures using blocks (base 10 blocks, unifix cubes, rainbow cubes) or sugar cubes. Each cube will represent 1 cubic unit. The volume will be the number of cubes that you use to build the figure.
Once the figure is constructed, you can view it from the front, top, and side to draw the 2-d views. These views will be used to find the surface area.
img/img_orthographic_views_grid.gif
We can see that the rectangular prism has a length of 4 units, a width of 2 units, and a height of 3 units. It would take 24 cubes to build this prism:
V = l × w × h
V = (4 units)(2 units)(3 units)
V = 24 cubic units
Remember that a rectangular prism has three pairs of congruent faces: front and back, top and bottom, and left and right sides. The 2-d views show the three different faces, so their area can be doubled to find the surface area.
img/img_prism_surface_area.gif
Top and Bottom: 2(4 units × 3 units) = 2(12 units2) = 24 units2
Front and Back: 2(4 units × 2 units) = 2(8 units2) = 16 units2
Left and Right: 2(2 units × 3 units) = 2(6 units2) = + 12 units2
52 units2
We could also add the area of the three different views and double that amount:
2(4 x 3 + 4 x 2 + 2 x 3) =
2(12 + 8 + 6) =
2(26) = 52
This method will also work even if the figure is made up of two rectangular prisms:
img/img_orthographic_composite.gif
So, the surface area is still the total area of the 3 different sides doubled: Front - (4 × 3), Top - (4 × 2), Side - 5.
2(4 × 3 + 4 × 2 + 5) =
2(12 + 8 + 5) =
2(25) = 50
Project
1) Build each of the three solid figures shown below. If you do not have any blocks or sugar cubes, use the 3D views for the next step.
2) Draw the 2-d views of each solid figure.
The top view is above the front view.
The side view is to the right of the front view.
3) Find the surface area and volume of each solid figure.
Show the equations you used.
4) Repeat the steps above for three solid figures of your own (if you have access to blocks or sugar cubes).
img/img_prism_one_project.gif
img/img_prism_two_project.gif
img/img_prism_three_project.gifSo, the surface area is still the total area of the 3 different sides doubled: Front - (4 × 3), Top - (4 × 2), Side - 5.
2(4 × 3 + 4 × 2 + 5) =
2(12 + 8 + 5) =
2(25) = 50
Project
1) Build each of the three solid figures shown below. If you do not have any blocks or sugar cubes, use the 3D views for the next step.
2) Draw the 2-d views of each solid figure.
The top view is above the front view.
The side view is to the right of the front view.
3) Find the surface area and volume of each solid figure.
Show the equations you used.
4) Repeat the steps above for three solid figures of your own (if you have access to blocks or sugar cubes).
img/img_prism_one_project.gif
img/img_prism_two_project.gif
img/img_prism_three_project.gif
