Calculus

posted by .

Find the volume of the solid formed by revolving the region bounded by the graphs of y=4x^2 and y=16 about the x-axis. (Washer Volume)

  • Calculus -

    integral from y = 0 to y = 16 (origin to x = 2)
    find volume of outer cylinder of radius 16
    Vol - pi r^2 h = pi (16^2) (2)

    find volume generated by inner curve between x axis and y = 4 x^2
    Vinner = pi y^2 dx from 0 to 2
    = pi 16 * integral x^4 dx
    = 16 pi (32/5)

    then subtract the inner from the outer
    2 pi (16^2) - 16 pi (32/5)

    = 32 pi *16 - 32 pi *16/5

    = 32 pi (4/5) (16)

  • Calculus -

    Oh, double that to include the left side.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Calculus

    This problem set is ridiculously hard. I know how to find the volume of a solid (integrate using the limits of integration), but these questions seem more advanced than usual. Please help and thanks in advance! 1. Find the volume of …
  2. calculus

    Find the volume of the solid formed by revolving the region bounded by the graphs of y=3-(x^2) and y=2 about the line y=2
  3. calculus

    Find the volume of the solid generated by revolving the region bounded by the graphs of the equations and/or inequalities about the indicated axis. x = y(25 − y2)^1/2 x = 0 the y-axis
  4. Calculus

    1. Use cylindrical shells to compute the volume of the solid formed by revolving the region bounded by y= 2x and y = x^2 -3 about x= 6. 2. Find the volume of the solid formed by revolving the region bounded by y= e^x , y= e^-x, and …
  5. Can no one help?!

    1. Use cylindrical shells to compute the volume of the solid formed by revolving the region bounded by y= 2x and y = x^2 -3 about x= 6. 2. Find the volume of the solid formed by revolving the region bounded by y= e^x , y= e^-x, and …
  6. calculus

    find the volume of the solid generated by revolving the region bounded by the graphs of the equations y=2sqrtx, y=o, x=3 about the x-axis.
  7. Calculus

    Find the volume of the solid formed by revolving the region bounded by the graphs of y = x^2, x = 4, and y = 1 about the y-axis. I'm supposed to use this equation right?
  8. AP Calculus AB

    Find the volume of the solid formed by revolving the region bounded by the graphs of y = x^2, x = 4, and y = 1 about the y-axis 39pi/2 225pi/2 735pi/2 None of these I got 39pi/2
  9. Calculus

    I would like to know if my answers are correct: Disclaimer: We are allowed to keep our answers in formula form 1. Use the washer method to find the volume of the solid that is generated by rotating the plane region bounded by y=x^2 …
  10. Calculus

    find the volume of the solid formed by revolving the region bounded by the graphs of y=x^3 y=1 x=2 about the y-axis

More Similar Questions