A block in the shape of a parallelepiped of sides 1m × 2m × 3m lies on the surface. Which of the faces gives maximum stable block? A. 1 m × 2 m B. 2 m × 3 m C. 1 m × 3 m D. Equally stable on all faces

The correct answer is A. 1 m × 2 m.

A parallelepiped is a three-dimensional shape with six faces, each of which is a rectangle. The faces of a parallelepiped are parallel to each other, and the opposite faces are congruent.

The most stable position for a parallelepiped is when it is resting on its largest face. In this position, the parallelepiped has the greatest surface area in contact with the ground, and the weight of the parallelepiped is evenly distributed.

The face with dimensions 1 m × 2 m is the largest face of the parallelepiped, so it is the most stable position for the parallelepiped to rest on.

The other options are not as stable because they have smaller surface areas in contact with the ground. This means that the weight of the parallelepiped is not evenly distributed, and the parallelepiped is more likely to tip over.

Option B: The face with dimensions 2 m × 3 m is not as stable as the face with dimensions 1 m × 2 m because it has a smaller surface area in contact with the ground. This means that the weight of the parallelepiped is not evenly distributed, and the parallelepiped is more likely to tip over.

Option C: The face with dimensions 1 m × 3 m is not as stable as the face with dimensions 1 m × 2 m because it has a smaller surface area in contact with the ground. This means that the weight of the parallelepiped is not evenly distributed, and the parallelepiped is more likely to tip over.

Option D: The parallelepiped is not equally stable on all faces because the faces have different surface areas. The face with dimensions 1 m × 2 m has the largest surface area, so it is the most stable position for the parallelepiped to rest on.