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?

## Answer this Question

## Related Questions

- AP Calc - The base of a solid is bounded by y=|x|+a, <a<, and the line y=3...
- Calculus (cross section) - A solid has a base bounded by x^2_y^2=36. Find the ...
- Calculus - R is the region in the plane bounded below by the curve y=x^2 and ...
- Calculus - R is the region in the plane bounded below by the curve y=x^2 and ...
- Calculus - R is the region in the plane bounded below by the curve y=x^2 and ...
- Calculus (Volume of Solids) - A solid has, as its base, the circular region in ...
- calculus - The base of a solid consists of the region bounded by the parabola y=...
- Calculus - A solid has as its base a circular region in the xy plane bounded by ...
- calculus - The base of a solid is the region in the first quadrant bounded by ...
- AP Calc - The base of a solid is the region in the first quadrant bounded by the...