Posted by tyson on Wednesday, January 30, 2013 at 12:51pm.
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?

Calculus  Steve, Wednesday, January 30, 2013 at 3:05pm
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
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