Volumes by Slicing

1. 7.3 Volumes by Slicing 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 x-axis.

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

7. NO CALCULATOR Let R be the first quadrant region enclosed by the graph of a) Find the area of R in terms of k. • Find the volume of the solid generated when R is • rotated about the x-axis in terms of k. c) What is the volume in part (b) as k approaches infinity?

8. Let R be the first quadrant region enclosed by the graph of a) Find the area of R in terms of k.

9. Let R be the first quadrant region enclosed by the graph of • Find the volume of the solid generated when R is • rotated about the x-axis in terms of k.

10. Let R be the first quadrant region enclosed by the graph of c) What is the volume in part (b) as k approaches infinity?

11. 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.

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

13. 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

14. 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. Cross Sections

15. The base of a solid is the circle . Each section of the solid cut by a plane perpendicular to the x-axis is a square with one edge in the base of the solid. Find the volume of the solid in terms of a. (NO PI)

16. CALCULATOR REQUIRED

17. 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.

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.

19. 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

20. The base of a solid is a right triangle whose perpendicular sides have lengths 6 and 4. Each plane section of the solid perpendicular to the side of length 6 is a semicircle whose diameter lies in the plane of the triangle. The volume of the solid in cubic units is: a) 2pi b) 4pi c) 8pi d) 16pi e) 24pi

21. CALCULATOR REQUIRED

22. NO CALCULATOR

23. CALCULATOR REQUIRED

24. NO CALCULATOR

25. CALCULATOR REQUIRED

26. CALCULATOR REQUIRED