 # Section Volumes by Slicing

## Presentation on theme: "Section Volumes by Slicing"— Presentation transcript:

Section 8.2 - Volumes by Slicing
7.3 Solids of Revolution

Find the volume of the solid generated by revolving the regions

Find the volume of the solid generated by revolving the regions

Find the volume of the solid generated by revolving the regions

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

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

CALCULATOR REQUIRED

CALCULATOR REQUIRED

CALCULATOR REQUIRED Cross Sections

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.

CALCULATOR REQUIRED

NO CALCULATOR

NO CALCULATOR

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.

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.

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.