In this lesson's introduction, you saw how engineers use orthographic views of a helicopter and how the orthographic views compare to both an isometric view of the helicopter and photo of the prototype of the helicopter. In this section, you will investigate different ways to construct isometric views of a three-dimensional figure when you know the orthographic views.

Consider the three-dimensional object whose orthographic views are shown below.

Source: Isometric Drawing Tool, NCTM Illuminations

Use the Isometric Drawing Tool applet, linked from the image below, to construct the three-dimensional object with the given orthographic views.

• To start, click and drag a couple of cubes onto the isometric grid in the applet. This will help you establish the "Front" of the object, which will in turn generate the other perspectives for you. Considering that the orthographic views that are shown are the top, right, and front, and an isometric view can show 3 sides of a solid, those should be the 3 views you should be able to see on your isometric drawing.
• Open the "Instructions" tab to get help on the various tools.

Interactive popup. Assistance may be required. Click here for additional directions.




Source: Isometric Drawing Tool Perspective Image, NCTM Illuminations

Right click on the eye tool (it will be a pop-up) to view the perspectives and ensure that your illustration is accurate. Use the Unit Movement buttons to move the blocks into the appropriate location.

Interactive popup. Assistance may be required. Click here for additional directions.


• To save your work inside of the Isometric Drawing Tool Applet once you have finished, select the "Email" icon in the top right and send it to yourself or your instructor. You can choose the "Print" icon in the top right and print the page to keep in your notes. Alternatively, you may use your computer’s Snipping Tool or screen capture software or your device’s screen capture procedures in order to save an image of your work.

Conclusion Questions

• How many blocks did it take to create the three-dimensional block model?

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  Check Your Answer

  7

• Suppose that one single cube has a side length of three meters. What would the volume be of the single cube?

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  Check Your Answer

  27 cubic meters

• How could you find the volume of the three-dimensional block model that you created?

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  Check Your Answer

  You could determine the volume of one cube. Then knowing that there were 7 cubes of the same size that were used to create the object, you could multiply that volume by 7 to give you the volume for the entire object.

• What is the total volume of the three-dimensional block model that you created, assuming that the side length of a single cube is 3 meters?

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  Check Your Answer

  189 cubic meters

Pause and Reflect

Which orthographic view is the easiest for you to see from the isometric view?

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Check Your Answer

Different people see different views more easily. Some students see the front view more clearly when looking at the isometric view from the left-hand side of the figure since the front of the figure faces to the left-hand bottom of the screen.Some students see the front view more clearly when looking at the isometric view from the left-hand side. Some students see the right side view more clearly.

Practice

In the questions below, you are given the orthographic views of a three-dimensional figure. Match the views with the isometric view of the figure.

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Need a hint?

You may find it easier to begin with the isometric view and identify the orthographic views from the isometric perspective.

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Check Your Answer

1-A
2-D
3-B