Posted by **Morgan** on Monday, January 23, 2012 at 10:38pm.

Find the volume of the solid generated by revolving the triangular region with vertices (1,1), (b,1), and (1,h) about:

a) the x-axis

b) the y-axis

- Calculus II -
**Steve**, Tuesday, January 24, 2012 at 11:12am
If a<1 and b<1 we get

Using discs:

pi*Int(R^2 - r^2) dx [b,1]

R = 1

r = y = (a-1)(x-b)/(1-b) + 1

= pi/3 (a-1)(a+2)(b-1)

Using shells:

2pi*Int(rh)dy [a,1]

r = y

h = 1-x = 1 - [(1-b)(y-1)/(a-1) + b]

= pi/3 (a-1)(a+2)(b-1)

If a or b > 1, then change integration limits and (1-a) -> (a-1), but the answer is the same

Thank you, Wolframalpha!

- Calculus II - PS -
**Steve**, Tuesday, January 24, 2012 at 11:13am
oh - that's just around the x-axis. Good luck on the y-axis. By symmetry, the results should look quite similar.

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