Posted by **mike** on Sunday, October 28, 2012 at 6:42pm.

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 cross-sections perpendicular to the x-axis are squares.

- calculus -
**MathMate**, Sunday, October 28, 2012 at 7:12pm
"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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