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Section 5.3 - Volumes by Slicing 7.3 Solids of Revolution.

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Presentation on theme: "Section 5.3 - Volumes by Slicing 7.3 Solids of Revolution."— Presentation transcript:

1 Section Volumes by Slicing 7.3 Solids of Revolution

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

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

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 about the x-axis.bounded by

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

7 Let R be the first quadrant region enclosed by the graph of a) Find the area of R in terms of k. b)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 b)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. b)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? c)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 b)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 c)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.


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