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January 29th, 2013, 08:36 AM   #1
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help setting these up-slicing

31. The vertex of a pyramid lies at the origin, and the base is perpendicular to the x-axis at x=4. The cross sections of the pyramid perpendicular to the x-axis are squares whose diagonals run from the curve y=-5x^2 to the curve y=5x^2.

33. The base of a solid is the circle x^2 + y^2 = a^2. Each section of the solid cut by a plane perpendicular to the x-axis is a square with one edge in the base of the solid. Find the volume of the solid.
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January 29th, 2013, 11:25 AM   #2
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Re: help setting these up-slicing

Quote:
Originally Posted by cheyb93
31. The vertex of a pyramid lies at the origin, and the base is perpendicular to the x-axis at x=4. The cross sections of the pyramid perpendicular to the x-axis are squares whose diagonals run from the curve y=-5x^2 to the curve y=5x^2.
So the length of each diagonal is . Now, if a square has sides of length s, it has diagonals of length . Setting that equal to , that is, so that . That means that each square has area
. Taking each square to have "thickness" dx, it has volume and integrating that from 0 to 4 will give the volume.

Quote:
33. The base of a solid is the circle x^2 + y^2 = a^2. Each section of the solid cut by a plane perpendicular to the x-axis is a square with one edge in the base of the solid. Find the volume of the solid.
For given x, then, y goes from to , length of . The square will have are .

That's all pretty standard. I am puzzled that you showed no attempt of your own.
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January 29th, 2013, 08:02 PM   #3
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Re: help setting these up-slicing

Our professor gave us one example on the board, only one homework problem on this topic, and there was very little instruction in the book. I am not sure why you are puzzled, but thanks anyway for helping.
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