Student Questions:

Consider the formula shown in blue for the volume of a solid of revolution using the shell method and rotating about the y - axis.

                                                          

1. What do a and b represent?

2. What symbolism in the integrand represents the circumference?

3. What symbolism in the integrand represents the height(length) of the shell?

4.  Explain in words the process of determining the volume of a solid when generated by revolving shells.

5. Sketch the curves 4*x - x^2 and 8x - 2x^2 .

6. Determine where these two graphs intersect and then focus on the enclosed region bewteen them.

7. Use the shell method to generate a volume about the y-axis and determine that volume's value.

8. Repeat the problem but this time revolve the enclosed region about the line x = -2.

9. Explain why shells will not work if you wish to generate the solid about the x-axis.

10. Challenge: Revolve the circle with equation:  (x-4)^2 + y^2 = 1 about the y-axis to produce the donut shape which is technically called a torus. Find the voulme of the donut by the shell method. Also, determine the same volume by the disk method. If all goes well, these two answers should be the same!