1. Section 5.3 - 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
bounded by
about the y-axis.

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. 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?
HINT:

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. 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.