SOLUTION: A bowl is designed by revolving completely the area enclosed by y = x^2- 1, y = 3 and x ≥ 0 around the axis. What is the volume of this bowl?

Algebra ->  Bodies-in-space -> SOLUTION: A bowl is designed by revolving completely the area enclosed by y = x^2- 1, y = 3 and x ≥ 0 around the axis. What is the volume of this bowl?      Log On


   

Question 771777: A bowl is designed by revolving completely the area enclosed by y = x^2- 1, y = 3 and x ≥ 0 around the axis. What is the volume of this bowl?
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


is a parabola with vertex at . is the horizontal line that passes through and that intersects the parabola, in the desired interval, at .

It will be convenient to write as a function of :





Rotate the parabola, then consider a thin disk with radius . The volume of this disk is

Integrate from -1 to 3





John

My calculator said it, I believe it, that settles it
The Out Campaign: Scarlet Letter of Atheism