# Volumes, Strang

rocomath
I have a simple question on the set-up of a triangular prism.

Strang, Ch. 8: Applications of the Integral

pdf page 4 (bottom) and correlates with example 5 on pdf page 5
http://ocw.mit.edu/ans7870/resources/Strang/Edited/Calculus/8.1-8.3.pdf [Broken]

How is he getting the length of $$1-\frac x h$$

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Vid
Look at the last figure on 8.3. 6(1-x/h)^2 is the area of a cross section at x. The line going through the height of each triangle is H = 3(1 - x/h). Using similar triangles the base of each triangle is B = 4(1-x/h). Thus, area = A(x) = 1/2*B*H = 6(1-x/h)^2. The volume is then obtained by adding together all the areas of each cross section which is the integral of A(x) from x = 0 to x =h.