Question

What is the center of mass of a cone with a hemisphere?

1) At the apex of the cone
2) At the center of the hemisphere
3) At the centroid of the combined shape
4) Cannot be determined

Answer 1

The center of mass of a cone with a hemisphere is at the centroid of the combined shape.

Step-by-step explanation:

The location of the center of mass of a cone with a hemisphere is at the centroid of the combined shape.

To find the centroid, we can consider the two shapes separately and then find their individual centroids. The centroid of a cone is located one-fourth of the way up from its base, along its central axis. The centroid of a hemisphere is located at its geometric center.

Since the two shapes are combined, we can find the centroid of the combined shape by finding the weighted average of the individual centroids based on the mass distribution of each shape. In this case, since both shapes have uniform density and mass, the centroid of the combined shape will be the midpoint between the centroid of the cone and the centroid of the hemisphere.

Therefore, the correct answer is:

1. At the centroid of the combined shape