Goal: Find the center of mass of a solid in 3 dimensions
We already stated the formulas to calculate the center of mass of a solid in 3 dimensions. Let's solve an example.
Example
Suppose Q is a solid region bounded by the plane x + 2y + 3z = 0, the coordinates planes with density ϼ(x,y,z) = x²yz (see figure in the example in the previous post). Find the center of mass using decimal approximation. Use the mass found in the previous example.
Solution
Consider the same region Q and the density function ρ(x,y,z) = xy²z. Find the center of mass using the following figure used in this example.
