Calculus

The base of a solid in the region bounded by the graphs of y = e^-x, y = 0, and x = 0, and x = 1. Cross sections of the solid perpendicular to the x-axis are semicircles. What is the volume, in cubic units, of the solid?

Answers:
1)(pi/16)e^2
2)(pi/16)(1-1/e^2)
3)(pi/4)(1-1/e^2)
4)(pi/16)(e^2-1)

I'm so confused. I know the volume of a semicircle would be 1/2pir^2h. h would be dx and I think finding the radius is what's throwing me off. Can someone help?

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asked by Kait
  1. huh. You seem to have it in hand. The diameter of each semicircle is just y=e^-x, so

    v = ∫[0,1] πd^2/8 dx
    where d=y=e^-x
    v = ∫[0,1] π/8 e^(-2x) dx = π/16 (1 - 1/e^2)

    Too bad you couldn't show some of your work ...

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    posted by Steve

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