Ask questions and get helpful answers.

Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line.

x = 4(square root of (3y)), x = 0, y = 3;
about the y-axis

V=?????

  1. 👍
  2. 👎
  3. 👁
  4. ℹ️
  5. 🚩

1 answer

  1. x=4√(3y)
    x^2 = 48y

    To use discs, note that the radius of each disc is x, and the thickness is dy, so

    v = ∫[0,3] πx^2 dy
    = 48π∫[0,3] y dy
    = 216π

    To use shells, each shell has radius x, and height 3-y, so

    v = ∫[0,12] 2πx(3-y) dx
    = 2π∫[0,12] x(3-x^2/48) dx
    = 216π

    1. 👍
    2. 👎
    3. ℹ️
    4. 🚩

Answer this Question

Related Questions

Still need help?

You can ask a new question or browse existing questions.