Section 8.2 - Volumes by Slicing 7.3 Solids of Revolution.

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Presentation transcript:

Section Volumes by Slicing 7.3 Solids of Revolution

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

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

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

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

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

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? NO CALCULATOR

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 b)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?

CALCULATOR REQUIRED

NO CALCULATOR Cross Sections

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. CALCULATOR REQUIRED

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 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

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.

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 R a)Setup but do not evaluate the integral representing the volume of the solid generated when R is revolved around the x-axis. b)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.

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 a)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. b)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.

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) 2.79 b) 2.82 c) 2.85 d) 2.88 e) 2.91

CALCULATOR REQUIRED

NO CALCULATOR

CALCULATOR REQUIRED

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.