Posted by **Anon** on Sunday, March 16, 2014 at 6:13pm.

The base of a solid is bounded by y =|x|+a, 0<a<3, and the line y=3. find in cu. units in terms of a, the volume of the solid if every cross section perpendicular to the y-axis is an equilateral triangle.

- AP Calculus -
**Steve**, Monday, March 17, 2014 at 12:00am
each cross-section has base 2x and altitude x√3

So, we want to add up all those triangles

v = ∫[a,3] 1/2 * 2x * x√3 dy

= √3 ∫[a,3] x^2 dy

But,

y = |x| + a

y-a |x|

(y-a)^2 = x^2

v = √3 ∫[a,3] (y-a)^2 dy

and now it's cake, right?

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