How do you find the volume of the solid with base region bounded by the triangle with vertices #(0,0)#, #(1,0)#, and #(0,1)# if cross sections perpendicular to the #x#-axis are squares?
Start with a picture of what we are dealing with:
So we have a pyramid, the volume of which is given by the formula
Volume of given shape
If you are uncertain of where the formula for the volume came from, consider the following image:
The pyramid (in red) with volume