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

The ellipse x2/9+y2/4=1 is revolved about the x-axis. Find the volume of the ellipsoid.

  1. 8 π 25.13
  2. 16 π 50.27
  3. 32 π 100.53
  4. 12 π 37.7

Answer

B. 16 π 50.27

Solution

V=π -334≤ft(1-x2/9 )dx=8π≤ft[x-x3/27 ]03=8π(3-1)=16π.

More Applications: Volume, Arc Length, Surface Area questions

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

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