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 ...
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?
1 answer
1 answer