The line through (0, 0) and (1, 2) has equation .
Each cross section has a leg in the -plane whose length is the horizontal distance from the
-axis to the line
, which is
.
The cross sections are isosceles right triangles, so the legs that lie perpendicular to the -plane have the same length as the legs *in* the
-plane, hence these triangles haves bases and heights equal to
. Then the area of each cross section is
where the cross sections are generated over the interval .
The volume of the solid is then