(a) Write down the conversion formula from the Cartesian coordinate to Spherical Coordinate and vice versa. (b) Using Cylindrical coordinate system, find the volume of a solid G that is bounded above by the hemisphere z = /16 – y² – x², below by the plane z = 1, and laterally by the cylinder x? + y? = 4. %3D

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.CT: Test
Problem 8CT: Determine whether the statement is true or false. a A right circular cone has exactly two bases. b...
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(a) Write down the conversion formula from the Cartesian coordinate to Spherical Coordinate and vice
versa.
(b) Using Cylindrical coordinate system, find the volume of a solid G that is bounded above by the
hemisphere

(a) Write down the conversion formula from the Cartesian coordinate to Spherical Coordinate and vice
versa.
(b) Using Cylindrical coordinate system, find the volume of a solid G that is bounded above by the
hemisphere z = /16 – y2 – x2, below by the plane z = 1, and laterally by the cylinder x? + y? = 4.
Transcribed Image Text:(a) Write down the conversion formula from the Cartesian coordinate to Spherical Coordinate and vice versa. (b) Using Cylindrical coordinate system, find the volume of a solid G that is bounded above by the hemisphere z = /16 – y2 – x2, below by the plane z = 1, and laterally by the cylinder x? + y? = 4.
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