The equation of a three-dimensional figure in rectangular coordinates along with its sketch are shown below. Which among the following is the correct integral expression for the volume of the space bound by the surface and the through- origin axis planes as shown in cylindrical coordinates? x? + 2y? + 2z – 5 = 0 y 5z- (cos 0y 2(sin 0)*) So sin 2 V5 rdrdedr 5-2z (cas 0)2+2(stn )2) S S So rdrdodz rv5 p5 v2(cos ' V5)° 5z (cos 0)°_2(sin 0)*) So rdrdodx 5- cos 0 2y V2 sin I So rdrdody

Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter10: Analytic Geometry
Section10.1: The Rectangular Coordinate System
Problem 41E: Find the exact lateral area of each solid in Exercise 40. Find the exact volume of the solid formed...
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The equation of a three-dimensional figure in rectangular coordinates along with
its sketch are shown below. Which among the following is the correct integral
expression for the volume of the space bound by the surface and the through-
origin axis planes as shown in cylindrical coordinates?
x? + 2y? + 2z – 5 = 0
y
Sz- (cos 0 2(sin 0)*)
sin
V5
rdrdedr
5-2z
(cas 0)+2(sin )2)
S S So
rdrdodz
rv5 p5 v2(cos ' 5)° 5z (cos 0)°_2(sin 0)*)
So
rdrdodx
5 cos 0- 2y
V2 sin 1
So
rdrdedy
Transcribed Image Text:The equation of a three-dimensional figure in rectangular coordinates along with its sketch are shown below. Which among the following is the correct integral expression for the volume of the space bound by the surface and the through- origin axis planes as shown in cylindrical coordinates? x? + 2y? + 2z – 5 = 0 y Sz- (cos 0 2(sin 0)*) sin V5 rdrdedr 5-2z (cas 0)+2(sin )2) S S So rdrdodz rv5 p5 v2(cos ' 5)° 5z (cos 0)°_2(sin 0)*) So rdrdodx 5 cos 0- 2y V2 sin 1 So rdrdedy
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