AP Calculus

posted by .

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 -

    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?

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Calculus

    R is the region in the plane bounded below by the curve y=x^2 and above by the line y=1. (a) Set up and evaluate an integral that gives the area of R. (b) A solid has base R and the cross-sections of the solid perpendicular to the …
  2. Calculus

    R is the region in the plane bounded below by the curve y=x^2 and above by the line y=1. (a) Set up and evaluate an integral that gives the area of R. (b) A solid has base R and the cross-sections of the solid perpendicular to the …
  3. Calculus

    R is the region in the plane bounded below by the curve y=x^2 and above by the line y=1. (a) Set up and evaluate an integral that gives the area of R. (b) A solid has base R and the cross-sections of the solid perpendicular to the …
  4. Calculus

    A solid has as its base a circular region in the xy plane bounded by the graph of x^2 + y^2 = 4. Find the volume of a solid if every cross section by a plane perpendicular to the x-axis is an isosceles triangle with base on the xy …
  5. Calculus (Volume of Solids)

    A solid has, as its base, the circular region in the xy-plane bounded by the graph of x^2 + y^2 = 4. Find the volume of the solid if every cross section by a plane perpendicular to the x-axis is a quarter circle with one of its radii …
  6. calculus

    The base of a solid consists of the region bounded by the parabola y=rootx, the line x=1 and the x-axis. Each cross section perpendicular to the base and the x-axis is a square. Find the volume of the solid.
  7. AP Calc

    The base of a solid is bounded by y=|x|+a, <a<, 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.
  8. Calculus (cross section)

    A solid has a base bounded by x^2_y^2=36. Find the volume of the solid if every plane section perpendicular to the diameter is an isosceles triangle whose base is on the circle and whose height is 4 units
  9. calculus

    The base of a solid is the region in the first quadrant bounded by the graph of y = 3/(e^x) , the x-axis, the y-axis, and the line x=2. Each cross section of this solid perpendicular to the x-axis is a square. What is the volume of …
  10. Calculus

    A base of a solid is the region bounded by y=e^-x, the x axis, the y axis, and the line x=2. Each cross section perpendicular to the x-axis is a square Find the volume of the solid

More Similar Questions