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

The region bounded by y=x2, x=0, x=2, and the x-axis is revolved about the x-axis. Find the volume generated.

  1. 32π/5 20.11
  2. 16π/5
  3. 64π/5
  4. 8π

Answer

A. 32π/5 20.11

Solution

V=π 02(x2)2,dx=π 02x4,dx=π≤ft[x5/5 ]02=32π/5 20.11.

More Applications: Volume, Arc Length, Surface Area questions

  1. The region bounded by y=sqrt(x), x=0, and x=4 is revolved about the x-axis. Find the volume generated.
  2. The region bounded by y=x, x=0, and y=3 is revolved about the y-axis. Find the volume generated.
  3. Find the length of the arc of the curve y=x3/2 from x=0 to x=4.
  4. Find the surface area generated by revolving the line y=x from x=0 to x=3 about the x-axis.
  5. Find the length of the arc of y= 23x3/2 from x=0 to x=3.
  6. The circle (x-5)2+y2=4 is revolved about the y-axis to form a torus. Find its volume.
  7. Find the area of the surface generated by revolving y=2sqrt(x), 0≤ x≤3, about the x-axis.
  8. Find the area of the surface generated by revolving y=x3, 0≤ x≤1, about the x-axis.
  9. Find the length of the catenary y=5 x5 from x=0 to x=5.
  10. Find the length of the curve y= ( x) from x=0 to x= π4.

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