Posted by mike on Sunday, October 28, 2012 at 6:42pm.
"The solid whose base is the region and whose cross-sections perpendicular to the x-axis are squares."
means that z=2y
but since y=2sqrt(1-x^2) (on the circle), so z=2sqrt(1-x^2)
For example, at x=0, z=1,
at x=1, z=0.
The volume of the solid is then
∫∫∫dx dy dz
where the limits of integration are
for z: 0 to 2sqrt(1-x^2)
for y: -sqrt(1-x^2) to sqrt(1-x^2)
for x: -1 to 1
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