Volume of revolution
Task
The volume of a glass can be modelled by rotating the function (x, f(x) in cm) around the y-axis. The volume of the glass should be 500 ml. Estimate the height of the glass.
Hint: Use the formula to calculate the volume of revolution around the x-axis of the portion of f(x) in the x-interval [a, b].
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Instructions
| 1. | Enter the function into the Input Bar and press Enter. |
| Note: The graph of f(x) will be displayed in the Graphics View. | |
| 2. | Calculate the inverse of f(x) using the command . |
| 3. | Press the More button and select Add label to label the inverse of f(x) with g. |
| 4. | Use the formula from the hint to calculate the volume of revolution around the x-axis of f(x) in the x-interval [0,h], where h is the height of the glass. |
| | Enter the command into the Input Bar and press Enter. |
| 5. | As the volume should be 500 ml, solve the equation . |
| | Therefore use the label you gave to the Integral and enter the command . |
| 6. | Press the  numeric toggle button to show the numeric solution. As result, the height of the glass is about 13.16 cm. |
| | Note: It is also possible to use more commands in one input. For example Steps 4 and 5 can be done by entering . GeoGebra CAS Calculator will automatically add a right parenthesis ) when entering your command with a left parenthesis (. |
