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].

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 (.