Engineering Board Exam Reviewer · Applications: Volume, Arc Length, Surface Area · medium

The region bounded by y=x and y=x2 is revolved about the line x=2. Find the volume generated.

  1. π/4 0.79
  2. π/2 1.57
  3. π 3.14
  4. 3 π/2 4.71

Answer

B. π/2 1.57

Solution

Shells: radius 2-x, height x-x2. V=2π 01(2-x)(x-x2),dx=2π 01≤ft(2x-3x2+x3 )dx=2π≤ft(1-1+ 14 )=π/2.

More Applications: Volume, Arc Length, Surface Area questions

  1. The ellipse x2/9+y2/4=1 is revolved about the x-axis. Find the volume of the ellipsoid.
  2. The region bounded by y=x3, the y-axis, and y=8 is revolved about the y-axis. Find the volume generated.
  3. The region under y=e-x for x≥0 is revolved about the x-axis. Find the volume of the resulting solid.
  4. The region bounded by y=x and y=x2 is revolved about the x-axis. Find the volume of the solid generated.
  5. The region bounded by y=x2, x=0, x=2, and the x-axis is revolved about the x-axis. Find the volume generated.
  6. The region bounded by y=sqrt(x), x=0, and x=4 is revolved about the x-axis. Find the volume generated.
  7. The region bounded by y=x, x=0, and y=3 is revolved about the y-axis. Find the volume generated.
  8. Find the length of the arc of the curve y=x3/2 from x=0 to x=4.
  9. Find the surface area generated by revolving the line y=x from x=0 to x=3 about the x-axis.
  10. Find the length of the arc of y= 23x3/2 from x=0 to x=3.

All Applications: Volume, Arc Length, Surface Area questions