GATE CS 2023 Q.5: Spatial Aptitude

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

The surface of the object must be concave everywhere.

The surface of the object must be convex everywhere.

The surface of the object may be concave in some places and convex in other places.

The object can have edges, but no corners.

Official answer and solution

Official answer: C
From: Official GATE 2023 answer key

Solution

Consider the geometric properties and local curvature of smooth 3-dimensional surfaces.

A smooth 3-dimensional object (such as a dumbbell, a torus, or an undulating vase) is differentiable everywhere without sharp edges or corners. The surface can have positive Gaussian curvature (convex regions), negative Gaussian curvature (saddle or concave regions), and zero Gaussian curvature (cylindrical or planar regions). Therefore, a smooth 3D object may be concave in some regions and convex in others.

Final answer

Option (C)

Common trap

Believing a smooth object must be globally convex like a sphere.

The answer is the one in the official GATE answer key. The solution is this site's own explanation.

Source

Paper: GATE 2023 Computer Science and Information Technology (CS)
Question: 5 of 65
Section: General Aptitude

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