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

The region bounded by y=x3, the y-axis, and y=8 is revolved about the y-axis. Find the volume generated.

  1. 96 π/5 60.32
  2. 32 π/5 20.11
  3. 96 π/7 43.08
  4. 48 π/5 30.16

Answer

A. 96 π/5 60.32

Solution

Disks: x=y1/3, so V=π 08y2/3dy=π· 35≤ft[y5/3 ]08=3π/5(32)=96π/5.

More Applications: Volume, Arc Length, Surface Area questions

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

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