The vertical cross-section of a solid is shown below has 10 in every side angle find the volume of the solid that is formed when the shape is rotated around the vertical line marked 12 units. show your work.

I think I know what it forms - a cone!!

I'm guessing that the angles at the end are 10 degrees so that would make angle CAB equal 5 degrees.
Line AB would be the radius of the "upper cone".
Line BC is 12/2 or 6
tangent (A) = BC / AB
tangent (5) = 6 / AB
AB = 6 / tan(5)
AB = 6 / 0.087489
AB = 68.58 which is the radius of the "upper cone".
Cone Volume = (PI * radius^2 * height) / 3
Cone Volume = (PI * 68.58 * 68.58 * 6) / 3
Cone Volume = 29,551
That is just the "upper cone volume.  So, we multiply  29,551 * 2
and get 59,102 which is the volume of the entire solid.
 
Source for cone volume:
http://www.1728.org/volcone.htm