Posted by mike on .
the region bounded by the quarter circle (x^2) + (y^2) =1. Find the volume of the following solid.
The solid whose base is the region and whose crosssections perpendicular to the xaxis are squares.

calculus 
MathMate,
"The solid whose base is the region and whose crosssections perpendicular to the xaxis are squares."
means that z=2y
but since y=2sqrt(1x^2) (on the circle), so z=2sqrt(1x^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(1x^2)
for y: sqrt(1x^2) to sqrt(1x^2)
for x: 1 to 1