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Section 8.2 - Volumes by Slicing

Section 8.2 - Volumes by Slicing. 7.3. Solids of Revolution. Find the volume of the solid generated by revolving the regions. bounded by. about the x-axis. Find the volume of the solid generated by revolving the regions. bounded by. about the x-axis.

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Section 8.2 - Volumes by Slicing

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  1. Section 8.2 - Volumes by Slicing 7.3 Solids of Revolution

  2. Find the volume of the solid generated by revolving the regions bounded by about the x-axis.

  3. Find the volume of the solid generated by revolving the regions bounded by about the x-axis.

  4. Find the volume of the solid generated by revolving the regions about the y-axis. bounded by

  5. Find the volume of the solid generated by revolving the regions bounded by about the line y = -1.

  6. CALCULATOR REQUIRED The volume of the solid generated by revolving the first quadrant region bounded by the curve and the lines x = ln 3 and y = 1 about the x-axis is closest to a) 2.79 b) 2.82 c) 2.85 d) 2.88 e) 2.91

  7. CALCULATOR REQUIRED

  8. CALCULATOR REQUIRED

  9. CALCULATOR REQUIRED Cross Sections

  10. Let R be the region marked in the first quadrant enclosed by the y-axis and the graphs of as shown in the figure below • Setup but do not evaluate the • integral representing the volume • of the solid generated when R • is revolved around the x-axis. R • Setup, but do not evaluate the • integral representing the volume • of the solid whose base is R and • whose cross sections perpendicular • to the x-axis are squares.

  11. CALCULATOR REQUIRED

  12. NO CALCULATOR

  13. NO CALCULATOR

  14. CALCULATOR REQUIRED Let R be the region in the first quadrant under the graph of a) Find the area of R. • The line x = k divides the region R into two regions. If the • part of region R to the left of the line is 5/12 of the area of • the whole region R, what is the value of k? • Find the volume of the solid whose base is the region R • and whose cross sections cut by planes perpendicular • to the x-axis are squares.

  15. Let R be the region in the first quadrant under the graph of a) Find the area of R.

  16. Let R be the region in the first quadrant under the graph of • The line x = k divides the region R into two regions. If the • part of region R to the left of the line is 5/12 of the area of • the whole region R, what is the value of k? A

  17. Let R be the region in the first quadrant under the graph of • Find the volume of the solid whose base is the region R • and whose cross sections cut by planes perpendicular • to the x-axis are squares.

  18. Let R be the region in the first quadrant bounded above by the graph of f(x) = 3 cos x and below by the graph of • Setup, but do not evaluate, an integral expression in terms of • a single variable for the volume of the solid generated when • R is revolved about the x-axis. • Let the base of a solid be the region R. If all cross sections • perpendicular to the x-axis are equilateral triangles, setup, • but do not evaluate, an integral expression of a single • variable for the volume of the solid.

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