Exploring volumes of revolution


Explore the shape create when you revolved a function around the x-axis.

Please do the following: Use the two sliders to see information about the solid in the 3D window. Use the 3D window to rotate the view. Change the left and right endpoints. Change the function. Use all of this to help answer the general questions about volumes of revolutions.

In general, what is the radius of each circle?

In terms of your answer above, what is the area of each circle?

Between what x values do these circles appear?

For three different functions, show the set up of the integral that will give you the volume when your function is revolved around the x-axis. Check to see that your integral will give you the volume noted in the applet.