Calculus
posted by tyson .
The base of a certain solid is the triangle with vertices at (14,7),(7,7) and the origin. Crosssections perpendicular to the yaxis are squares. What is the volume of this solid?

Integrating along y, the area of each crosssection is (2x)^2, so
v = ∫[0,7] (2x)^2 dy
Now, x = (7y), so
v = ∫[0,7] (2(7y))^2 dy
= 4* 1/3 (y7)^3 [0,7]
= 1372/3