3)Find the centroid of the upper half of a sphere of radius 1, that is, ofthe set of points in R³ where x² + y² + z² = 1 and z > 0. Use symmetry andgeometry.Formulas:SS F(x, y, z)dS = SS f(x, y, z)||Vh||-dA%3D|Vh · k|SDSSF nds = SSF.Vh-dA|Vh · k|SDArea (cylinder)=2rrhVolume (Cylinder)=rr²hArea (Sphere)=4ar²Volume (Sphere)=Tr³Theorems:ƒF•dF = S[s(V×F). Tdsf\beg|endSVf •d7de')dAдуӘР.SPdx + Qdy = [Sp(;

Given the upper half of the sphere with radius 1, that is x2+y2+z2=1,z≥0. Find the centroid x¯,y¯,z¯…

Answered: 3) . Find the centroid of the upper…

3) . Find the centroid of the upper half of a sphere of radius 1, that is, of the set of points in R3 where x² + y² + z² = 1 and z > 0. Use symmetry and geometry.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter9: Systems Of Equations And Inequalities

Section: Chapter Questions

Problem 12T

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Question

100%

3)
Find the centroid of the upper half of a sphere of radius 1, that is, of
the set of points in R³ where x² + y² + z² = 1 and z > 0. Use symmetry and
geometry.
Formulas:
SS F(x, y, z)dS = SS f(x, y, z)
||Vh||
-dA
%3D
|Vh · k|
S
D
SSF nds = SS
F.Vh
-dA
|Vh · k|
S
D
Area (cylinder)=2rrh
Volume (Cylinder)=rr²h
Area (Sphere)=4ar²
Volume (Sphere)=Tr³
Theorems:
ƒF•dF = S[s(V×F). Tds
f\beg
|end
SVf •d7
de'
)dA
ду
ӘР.
SPdx + Qdy = [Sp(;

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