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

The region bounded by y=sqrt(x), the x-axis, and x=4 is revolved about the line y=2. Find the volume generated.

  1. 16 π/3 16.76
  2. 64 π/3 67.02
  3. 40 π/3 41.89
  4. 8 π 25.13

Answer

C. 40 π/3 41.89

Solution

Washers: outer radius 2, inner radius 2-sqrt(x). V=π 04≤ft[4-(2- x)2 ]dx=π 04≤ft(4 x-x )dx=π≤ft(64/3-8 )=40π/3.

More Applications: Volume, Arc Length, Surface Area questions

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

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