convex polyhedron is the shape with finite volume and infinite surface area.
shape with finite volume and infinite surface area?
convex polyhedron
na
na
since the horn has finite volume but infinite surface area, there is an apparent paradox that the horn could be filled with a finite quantity of paint and yet that paint would not be sufficient to coat its inner surface. the paradox is resolved by realizing that a finite amount of paint can in fact coat an infinite surface area — it simply needs to get thinner at a fast enough rate. (much like the series gets smaller fast enough that its sum is finite.) in the case where the horn is filled with paint, this thinning is accomplished by the increasing reduction in diameter of the throat of the horn.
gabriel's horn