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The base of a solid is bounded by y=x^1/2, x=1, x=4, and y=0. What is the volume if the solid has square cross sections perpendicular to the x axis?

I got 15pi/2, but I'm not sure that's right. Could anyone help me find the right answer? the cross sections are confusing me. thank you!

Julia
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Invoke Cavaleri's Prinicple: To get the volume of this solid, integrate the area of the slice on $[1,4]$. You should not get a $\pi$ as a result.

ncmathsadist
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  • Thank you! that makes much more sense. If you don't mind me asking, so I can tell the difference in the future, where are you supposed to use the "disk" method? Is it only when the axis of revolution touches the curve or when it doesn't? – Julia Apr 09 '21 at 18:33
  • That is Cavaleri's principle when the slice is circular because you are rotating about a line. – ncmathsadist Apr 09 '21 at 19:34