Discussion
Looking at the surface of a smooth 3-dimensional object from the outside, which one of the following options is TRUE?
Answer: C
The true statement is that the surface may be concave in some places and convex in other places.
A smooth closed object such as a peanut shell, a dumbbell or a bean bulges outwards in most places but curves inwards at its waist, so a surface can mix both kinds of curvature. Nothing about being smooth or 3-dimensional forces one kind everywhere.
'Convex everywhere' holds for a sphere or an egg but is not required, so 'must' makes it false. 'Concave everywhere' is impossible for a closed bounded object seen from outside, since its outermost points must bulge outwards. 'Edges, but no corners' contradicts smoothness: a smooth surface has neither edges nor corners.
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