Calculus

The base of a solid in the xy-plane is the circle x^2+y^2 = 16. Cross sections of the solid perpendicular to the y-axis are semicircles. What is the volume, in cubic units, of the solid?

a. 128π/3
b. 512π/3
c. 32π/3
d. 2π/3

  1. 👍 0
  2. 👎 0
  3. 👁 1,996
  1. <<Cross sections of the solid perpendicular to the y-axis are semicircles>>
    Somehow, I am not visulizing this. so the base of the solid is in the xy plane, so its altitude must be in the k direction. For the k direction to be semicircles, the shape of the solid has to be a semisphere.

    the radius is 4. The volume of the semisphere then is 1/2 the sphere of radius 4,
    volume= 1/2 * 4/3 PI 4^3

    1. 👍 0
    2. 👎 0
  2. Each semicircle resting on the x-y plane has radius x=√(16-y^2). Adding up all the slices, and using symmetry, we have

    v = 2∫[0,4] 1/2 πr^2 dy
    = π∫[0,4] (16-y^2) dy = 128π/3

    bobpursley's solution is much more intuitive and geometric, though, eh?

    1. 👍 5
    2. 👎 0

Respond to this Question

First Name

Your Response

Similar Questions

  1. Calculus

    The base of a solid is the circle x2 + y2 = 9. Cross sections of the solid perpendicular to the x-axis are equilateral triangles. What is the volume, in cubic units, of the solid? 36 sqrt 3 36 18 sqrt 3 18 The answer isn't 18 sqrt

  2. calculus

    Find the volume V of the described solid S. The base of S is a circular disk with radius 2r. Parallel cross-sections perpendicular to the base are squares.

  3. calculus review please help!

    1) Find the area of the region bounded by the curves y=arcsin (x/4), y = 0, and x = 4 obtained by integrating with respect to y. Your work must include the definite integral and the antiderivative. 2)Set up, but do not evaluate,

  4. Calculus

    Find the volume of the solid whose base is the circle x^2+y^2=64 and the cross sections perpendicular to the x-axis are triangles whose height and base are equal. Find the area of the vertical cross section A at the level x=7.

  1. Calculus

    The base of a solid is the circle x^2 + y^2 = 9. Cross sections of the solid perpendicular to the x-axis are squares. What is the volume, in cubic units, of the solid? A. 18 B. 36 C. 72 D. 144 Please help. Thank you in advance.

  2. Calculus 2

    Find the volume of the solid whose base is the semicircle y= sqrt(1− x^2) where −1≤x≤1, and the cross sections perpendicular to the x -axis are squares.

  3. Calculus

    The base of a solid is bounded by the curve y=sqrt(x+1) , the x-axis and the line x = 1. The cross sections, taken perpendicular to the x-axis, are squares. Find the volume of the solid a. 1 b. 2 c. 2.333 d. none of the above I

  4. Calculus

    The base of a solid is the circle x^2 + y^2 = 9. Cross sections of the solid perpendicular to the x-axis are equilateral triangles. What is the volume, in cubic units, of the solid? 36√3 36 18√3 18

  1. calculus

    Find the volume V of the described solid S. The base of S is an elliptical region with boundary curve 9x2 + 25y2 = 225. Cross-sections perpendicular to the x-axis are isosceles right triangles with hypotenuse in the base.

  2. Calculus

    The base of a certain solid is the triangle with vertices at (-14,7),(7,7) and the origin. Cross-sections perpendicular to the y-axis are squares. What is the volume of this solid?

  3. Calculus I

    The base of a solid is the circle x^2 + y^2 = 9. Cross sections of the solid perpendicular to the x-axis are squares. What is the volume, in cubic units, of the solid?

  4. calculus

    The base of a certain solid is the triangle with vertices at (−6,3), (3,3), and the origin. Cross-sections perpendicular to the y-axis are squares. Then the volume of the solid?

You can view more similar questions or ask a new question.