As the number of edges a shape has increase, what happens to the volume?

Question

HELP!!!!!

yes, the same area

Answer 1

Assuming that the object is a regular polyhedron, the volume/surface area ratio should increase. If the surface area is kept constant, the volume would increase.

Think of a sphere as a polyhedron with an infinite number of edges. As you increase the number of edges, you will approach a sphere.

Answer 2

Since you are interested in volume, I assume you have a three-dimensional object. Start by imagining a cube with unit length edges. It has 12 edges and 6 surfaces. Determine the surface area and volume of that cube. Now consider a many sided object. Do you see that it is approaching the shape of a sphere? See how the area/volume ratio of the sphere compares to a cube and you might have your answer.

Answer 3

Are you assuming you have the same area but a shape with more edges?

Ok then, the volume is the same because the V is Base Area times Height and even if you have more edges you will have the same base area

Answer 4

Assuming you're talking about regular polygons, and the widest part of the polygon stays the same measure, the shape gets rounder. A ball is the most compact shape, so the area decreases.

That's why a 9-inch square pan uses up more cake batter than a 9-inch round pan.
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Okay, something's wrong with my explanation because it doesn't jive with eveybody else's. I'll get back to you.
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Aha, I can picture it now. Think of polygons inscribed in circle. The circle stays the same size. As the number of sides increases, the polygons do approach a circular shape, and they're still touching the circle, so the area expands.

Answer 5

Nothing, if the shape is a plane figure.

Answer 6

it increases