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**Section 8.2 - Volumes by Slicing**

7.3 Solids of Revolution

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**Find the volume of the solid generated by revolving the regions**

bounded by about the x-axis.

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**Find the volume of the solid generated by revolving the regions**

bounded by about the x-axis.

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**Find the volume of the solid generated by revolving the regions**

bounded by about the y-axis.

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**Find the volume of the solid generated by revolving the regions**

bounded by about the line y = -1.

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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) b) c) d) e) 2.91

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CALCULATOR REQUIRED

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CALCULATOR REQUIRED

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CALCULATOR REQUIRED Cross Sections

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**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.

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CALCULATOR REQUIRED

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NO CALCULATOR

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NO CALCULATOR

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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.

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**Let R be the region in the first quadrant under the graph of**

a) Find the area of R.

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**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

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**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.

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**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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