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

The base of a solid is the circle x2+y2=16. Cross sections perpendicular to the x-axis are squares. Find the volume of the solid.

  1. 512/3
  2. 256/3
  3. 2048/3
  4. 1024/3

Answer

D. 1024/3

Solution

Side of square =2sqrt(16-x2), so area =4(16-x2). V= -444(16-x2),dx=8≤ft(64-64/3 )=1024/3.

More Applications: Volume, Arc Length, Surface Area questions

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

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