A solid has, as its base, the circular region in the xy-plane bounded by the graph of x^2 + y^2 = 4. Find the volume of the solid if every cross section by a plane perpendicular to the x-axis is a quarter circle with one of its radii in the base.
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what does "one of its radii in the base" mean? Is its radius centered on the x-axis, or on a point of the circle, or what?
This is precisely why I posted, I thought that the wording of this practice problem might make sense to someone else, because it completely confused me.
After a lot of thinking, I figured that the solid of revolution was a hemisphere. It was created by rotating the quarter circle in the first quadrant around the y-axis perhaps. This resulted in a volume of (32/3)pi.
After a lot of thinking, I figured that the solid of revolution was a hemisphere. It was created by rotating the quarter circle in the first quadrant around the y-axis perhaps. This resulted in a volume of (32/3)pi.
You just integrate pi (4-y^2) from -2 to 2, and you will get 32pi/3.
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