The base of a certain solid is the triangle with vertices at (-14,7),(7,7) and the origin. Cross-sections perpendicular to the y-axis are squares. What is the volume of this solid?

Answer 1

Integrating along y, the area of each cross-section is (2x)^2, so

v = ∫[0,7] (2x)^2 dy
Now, x = (7-y), so
v = ∫[0,7] (2(7-y))^2 dy
= 4* 1/3 (y-7)^3 [0,7]
= 1372/3