How to Use Winplot to Create Solids of Revolution

How to Use Winplot to Create Solids of Revolution

1. Click on Window and drag down to 2 dim (since all of our graphs are originally two-dimensional). A blank grid should appear on the screen.

2. Within the grid window, click on Equa and drag down to Explicit. Another window should pop up in which you can type in your equation. In order to use powers, use the carat symbol (^). You may also use many of the same symbols that your calculator uses, such as "abs" for absolute value, the trig functions, "sqr" for square root, "int" for the greatest integer function. Click on the Edit menu and drag down to Library for other operations.

**Make sure to click in the box marked "lock interval" so that the graph is only over that particular domain.**

Clicking on OK should give you a graph of your function on the grid.

3. Go to the One menu and drag down to Revolve Surface. You should get the following box, which allows you to choose which line to revolve the function about. If you wish to revolve about a horizontal line, what are the values for a, b, and c? If you wish to revolve about a vertical line, what are the values for a, b, and c? Also change the values of arc start and arc stop to be the same x-values you used for low x and high x in the first box above. Click on see arc to see the portion of graph that will be rotated. Click on see surface. You should then see the 3-dimensional solid you have revolved.

4. In that solid of revolution window, go to the One menu and drag down to Slicer. Click on autocyc in the menu for current t-value. You should see the function move along the edge of the solid. In order to stop the movement of the revolution, type Q to quit. In order to rotate the solid to see different perspectives, use the up, down, left, and right arrow keys. Or, go to the View menu and drag down to Rotate and drag to the right to Make Tour. You should then see the solid from all views. In order to control the movement of the revolution, type Q to quit, S to slow the movement, or F to speed up the movement.

Now you try several graphs on your own. You may want to clear off the old function by going to the Equa menu and dragging down to Inventory. Then highlight the equation you want deleted and click on delete.

Find at least two functions that are solids, and find at least two functions that have a hole through the middle of the solid of revolution. You can open a Word document and copy each of the graphs into it so that all four surfaces are on the same sheet of paper for printing. To do this, click on the window showing your solid. Go to the File menu and drag down to Copy to clipboard. Then open a Word document, go to the Edit menu, and drag down to Paste. Then type in the equation you used and the axis of revolution next to each picture.