y^2-x^2=1, y=2; about the y-axis. Find the volume of the resulting solid by any method.

Question

y^2-x^2=1, y=2; about the y-axis.  Find the volume of the resulting solid by any method.

anonymous · Answer

Is there a lower boundary? Are you only considering the top half?

anonymous · Answer

Only the area where the two lines intersect.

anonymous · Answer

http://www3.wolframalpha.com/Calculate/MSP/MSP6291a321i51a73b265g0000329h1heh2i439b1b?MSPStoreType=image/gif&s=15&w=393&h=257&cdf=RangeControl

anonymous · Answer

Gotcha. Ok, I think you can do a disk method here - sum of many cylinders. Volume of cylinder = pir*r^2*h, r=x=sqrt(y^2-1), and h=dy. Integrate between y=1 and y=2.
That should do it.

anonymous · Answer

*(pir should be pi)

anonymous · Answer

Cool, I'm going to compute that and see if I get a plausible answer.  Thank You

anonymous · Answer

Ok, let me know what you get so I can check my answer.

anonymous · Answer

I get 4pi/3 or 4.19

anonymous · Answer

Same here. You can do a reasonableness check by comparing it to a similarly sized cone and use the volume formula for a cone.