Solid of rotation problem.

[TenaciousE]

Consider the solid obtained by rotating the region bounded by the given curves about the line y = 3.

Find the volume V of this solid.

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I've worked it about 5 times and I keep getting -.5pi, which of course, doesn't make sense for this problem. I have the large radius R as (1-3x) and the small radius r as (1-3sqrt(x)). I find the area by subtracting r from R and then use the FTC to find volume. I'm not sure what I'm doing wrong, so it would be great if someone could nudge me in the right direction.

 

[soroban]

Hello, TenaciousE!

Consider the solid obtained by rotation the region bounded by the given curves about the line y = 3.
. . \(\displaystyle y = 3x,\;y = 3\sqrt{x}\)
Find the volume of this solid.

I've worked it about 5 times and I keep getting -0.5pi, which of course, doesn't make sense for this problem.

I have the large radius R as (1 - 3x) and the small radius r as (1 - 3sqrt(x)).

What's with the 1's?

        |
      3 + - - - - - -
        |
        |
      1 +      ...*
        |   *:::* :
        | *:::*   :
        |*::*     :
        |:*       :
  - - - * - - - - + - - -
        |         1
        |

The two radii are: .\(\displaystyle 3 - 3x\,\text{ and }\,3 - 3\sqrt{x}\)