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The centroid of the polyhedron is ___________

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The centroid of the polyhedron is ___________

(a) the summation of the centroids of the pyramids

(b) the arithmetic mean of the centroids of the pyramids

(c) the weighted average of centroids of the pyramids

(d) the Pythagorean mean of centroids of the pyramids

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This intriguing question originated from Types of FVM Elements topic in portion Finite Volume Methods of Computational Fluid Dynamics

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The correct choice is (c) the weighted average of centroids of the pyramids

For explanation: The centroid of each of the sub-pyramids is calculated. Their volumes are also calculated. The weighted average of these centroids is calculated by using the volumes as the weights. This gives the centroid of the element.

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