15_5_22 - 22. Use spherical coordinates. The area of the...

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22. Use spherical coordinates. The area of the eighth-sphere is A = 1 8 ( 4 π a 2 ) = π a 2 2 sq. units. The moment about z = 0 is M z = 0 = ZZ z dS = Z π/ 2 0 d θ Z π/ 2 0 a cos φ a 2 sin φ d φ = π a 3 2 Z π/ 2 0 sin 2 φ 2 d φ = π a 3 4 . Thus z = M z = 0 A = a 2 . By symmetry, x = y = z , so the centroid of that part of the surface
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This note was uploaded on 03/08/2012 for the course MATH 120 taught by Professor Onurfen during the Spring '12 term at Middle East Technical University.

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