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

The region bounded by y=sqrt(x), x=0, and x=4 is revolved about the x-axis. Find the volume generated.

  1. 8π 25.13
  2. 16π
  3. 4π
  4. 32π/3

Answer

A. 8π 25.13

Solution

V=π 04 x,dx=π≤ft[x2/2 ]04=8π 25.13.

More Applications: Volume, Arc Length, Surface Area questions

  1. The region bounded by y=x, x=0, and y=3 is revolved about the y-axis. Find the volume generated.
  2. Find the length of the arc of the curve y=x3/2 from x=0 to x=4.
  3. Find the surface area generated by revolving the line y=x from x=0 to x=3 about the x-axis.
  4. Find the length of the arc of y= 23x3/2 from x=0 to x=3.
  5. The circle (x-5)2+y2=4 is revolved about the y-axis to form a torus. Find its volume.
  6. Find the area of the surface generated by revolving y=2sqrt(x), 0≤ x≤3, about the x-axis.
  7. Find the area of the surface generated by revolving y=x3, 0≤ x≤1, about the x-axis.
  8. Find the length of the catenary y=5 x5 from x=0 to x=5.
  9. Find the length of the curve y= ( x) from x=0 to x= π4.
  10. Find the length of the arc of y=x2/2- x/4 from x=1 to x=2.

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