Question

Looking at the surface of a smooth 3-dimensional object from the outside, which one of the following options is TRUE?

• A. The surface of the object must be concave everywhere.
• B. The surface of the object must be convex everywhere.
• C. The surface of the object may be concave in some places and convex in other places.
• D. The object can have edges, but no corners.

Hint:

In 3D geometry, a surface can exhibit both concave and convex properties at different locations.

Answer 1

The Correct Option is C

In a 3-dimensional object, the surface may have different geometries in different places. The surface can be concave in some areas (curved inward) and convex in others (curved outward). This means the surface is not necessarily one type everywhere, as shown by the option in (C).
- (A) is incorrect because the surface does not have to be concave everywhere.
- (B) is incorrect because a surface does not have to be convex everywhere.
- (D) is also incorrect, as the object can indeed have corners in certain geometric configurations (e.g., cubes).
Thus, the correct answer is (C), as the surface can be both concave and convex in different places.