Solid of Revolution Question

[Piefrenzy]

a

 

[stapel]

Find the volume of the solid generated by revolving the described region about the given axis:

The region enclosed above by the curve \(\displaystyle y\, =\, 1\, +\, \dfrac{x^2}{4}\), below by the x-axis, to the left by the y-axis, and to the right by the line x = 2, rotated about the y-axis.

I don't remember going over anything like this in class. I need some assistance.

Since your class hasn't yet covered the chapter on solids of revolution, you can probably safely ignore this question. But you might want to point this out to your instructor. Obviously, you can't legitimately be tested on stuff that your class hasn't yet gotten to.

 

[HallsofIvy]

Piefrenzy didn't say they hadn't covered this in class. He said, rather, that he "couldn't remember going over anything like this". And, he doesn't say what he means by "like this". It might be just that he doesn't remember what to do when the area rotated does not extend from the axis of rotation (here, the y- axis). The simplest way to do this is to calculate the volume of the area above \(\displaystyle y= 1+ \frac{x^2}{4}\), bounded above by y= 2, and on the left by the y-axis, then subtract that from the volume of a cylinder with radius 2 and height 2.