42 1. (Volumes of Solids with Known Cross-Sections). Sketch the solid bounded by the surfaces 2² +2²=9₁y² +2²=9 and find its volume. Hint: the surface 2² +2²=9 is a right circular cylinder, it is formed of straight lines perpendicular to the zz-plane coming through points of the circle √₂² +2²=9₁ y=0

Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter9: Surfaces And Solids
Section9.3: Cylinders And Cones
Problem 5E: For the right circular cylinder, suppose that r=5 in. and h=6 in. Find the exact and approximate a...
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The following problem is not obligatory, but it will bring you some bonus points if you solve it correctly.
1. (Volumes of Solids with Knoun Cross-Sections). Sketch the solid bounded by the surfaces
1² + z = 9, y +* = 9
42
and find its volume. Hint: the surface r² +z? = 9 is a right circular cylinder. it is formed of straight lines perpendicular
to the zz-plane coming through points of the circle
J²+z? = 9,
ly = 0
in the plane Orz; the surface y? + 2? = 9 is likewise a right circular cylinder. Think what axis (either the z-, or the y-,
or the z-axis) is best suitable to handle the problem.
Please give a complete solution to the problem.
In the two problems that follow in order to verify your sketches of surfaces of revolution, you can use the Wa website. For
instance, to see the surface of revolution obtained by revolving the quarter-circle
y = V9-7,
(0 sI 3)
(a semi-sphere of radius 3) produced by Wa, use the command
revolve y-sqrt( 9 - x*2 ), o -x - 3 about the x-axis
Transcribed Image Text:The following problem is not obligatory, but it will bring you some bonus points if you solve it correctly. 1. (Volumes of Solids with Knoun Cross-Sections). Sketch the solid bounded by the surfaces 1² + z = 9, y +* = 9 42 and find its volume. Hint: the surface r² +z? = 9 is a right circular cylinder. it is formed of straight lines perpendicular to the zz-plane coming through points of the circle J²+z? = 9, ly = 0 in the plane Orz; the surface y? + 2? = 9 is likewise a right circular cylinder. Think what axis (either the z-, or the y-, or the z-axis) is best suitable to handle the problem. Please give a complete solution to the problem. In the two problems that follow in order to verify your sketches of surfaces of revolution, you can use the Wa website. For instance, to see the surface of revolution obtained by revolving the quarter-circle y = V9-7, (0 sI 3) (a semi-sphere of radius 3) produced by Wa, use the command revolve y-sqrt( 9 - x*2 ), o -x - 3 about the x-axis
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