Section Volumes by Slicing

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Section Volumes by Slicing

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Presentation transcript:

Section 5.3 - 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.

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

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 line y = -1.

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:

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

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.

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

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.

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

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

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

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.