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

Find the area of the surface generated by revolving y=2sqrt(x), 0≤ x≤3, about the x-axis.

  1. 28 π/3 29.32
  2. 56 π/3 58.64
  3. 112 π/3 117.29
  4. 56 π/9 19.55

Answer

B. 56 π/3 58.64

Solution

y'=1/ x, so S=2π 03 2 xsqrt(1+ 1x),dx=4π 03sqrt(x+1),dx=4π· 23≤ft[(x+1)3/2 ]03=8π/3(8-1)=56π/3.

More Applications: Volume, Arc Length, Surface Area questions

  1. Find the area of the surface generated by revolving y=x3, 0≤ x≤1, about the x-axis.
  2. Find the length of the catenary y=5 x5 from x=0 to x=5.
  3. Find the length of the curve y= ( x) from x=0 to x= π4.
  4. Find the length of the arc of y=x2/2- x/4 from x=1 to x=2.
  5. The base of a solid is the region between y=x2 and y=8-x2. Cross sections perpendicular to the x-axis are semicircles whose diameters lie…
  6. 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.
  7. The region bounded by y=sqrt(x), the x-axis, and x=4 is revolved about the line y=2. Find the volume generated.
  8. The region bounded by y=x and y=x2 is revolved about the line x=2. Find the volume generated.
  9. The ellipse x2/9+y2/4=1 is revolved about the x-axis. Find the volume of the ellipsoid.
  10. The region bounded by y=x3, the y-axis, and y=8 is revolved about the y-axis. Find the volume generated.

All Applications: Volume, Arc Length, Surface Area questions