Solve the problem.
-Find the centroid of the first-octant portion of a solid ball of radius 3 centered at the origin.
A) $( \bar { x } , \bar { y } , \bar { z } ) = \left( \frac { 9 } { 5 } , \frac { 9 } { 5 } , \frac { 9 } { 5 } \right)$
B) $( \bar { x } , \bar { y } , \bar { z } ) = \left( \frac { 9 } { 8 } , \frac { 9 } { 8 } , \frac { 9 } { 8 } \right)$
C) $( \bar { x } , \bar { y } , \bar { z } ) = \left( \frac { 6 } { 5 } , \frac { 6 } { 5 } , \frac { 6 } { 5 } \right)$
D) $( \bar { x } , \bar { y } , \bar { z } ) = \left( \frac { 15 } { 8 } , \frac { 15 } { 8 } , \frac { 15 } { 8 } \right)$

Question

Solve the problem.
-Find the centroid of the first-octant portion of a solid ball of radius 3 centered at the origin. 
A) $( \bar { x } , \bar { y } , \bar { z } ) = \left( \frac { 9 } { 5 } , \frac { 9 } { 5 } , \frac { 9 } { 5 } \right)$
B) $( \bar { x } , \bar { y } , \bar { z } ) = \left( \frac { 9 } { 8 } , \frac { 9 } { 8 } , \frac { 9 } { 8 } \right)$
C) $( \bar { x } , \bar { y } , \bar { z } ) = \left( \frac { 6 } { 5 } , \frac { 6 } { 5 } , \frac { 6 } { 5 } \right)$
D) $( \bar { x } , \bar { y } , \bar { z } ) = \left( \frac { 15 } { 8 } , \frac { 15 } { 8 } , \frac { 15 } { 8 } \right)$

Quizplus · Accepted Answer

The centroid of a solid ball in the first octant is found by integrating over the volume of the octant. For a sphere of radius 3, the centroid coordinates are $( \bar { x } , \bar { y } , \bar { z } ) = \left( \frac { 9 } { 8 } , \frac { 9 } { 8 } , \frac { 9 } { 8 } \right)$.

Solve the Problem (xˉ,yˉ,zˉ)=(95,95,95)( \bar { x } , \bar { y } , \bar { z } ) = \left( \frac { 9 } { 5 } , \frac { 9 } { 5 } , \frac { 9 } { 5 } \right)(xˉ,yˉ​,zˉ)=(59​,59​,59​)

Solve the Problem $( \bar { x } , \bar { y } , \bar { z } ) = \left( \frac { 9 } { 5 } , \frac { 9 } { 5 } , \frac { 9 } { 5 } \right)$