Question

Using the piling method, which of the following can be constructed from polygons alone and discs alone

Answer 1

Answer:

All the mentioned can be constructed with the help of piling method. But, for construction of b and d we need a point as well.   

Step-by-step explanation:

a) Yes, a cube can be formed by stacking polygons. If we stack squares one upon another, then the resulting 3-D figure would be a cube.

b) Yes, a cone that does not include the point can be made by stacking disc. If we stack discs such that the discs are arranges in descending order then the resultant 3-D figure would be a cone that does not include a point.

c) Yes, a pyramid can be formed by stacking polygons.

If we stack squares such that they are arranged in descending order of their side length and stacked by a point on the top. Then the resultant figure would be a  pyramid that includes a vertex.

f) There are many types of prism. Fro example a rectangular prism can be constructed by simply stacking rectangle polygon on one another.

e) Yes, a cone can be formed by stacking disc.

We need to stack disks arranged in descending order of their radius stacked with a point on the top. The resulting figure would be a cone that includes a point.

f) Yes, a cylinder can be formed by stacking. We need to stack discs of same radius to get a cylinder.

Answer 2

Answer:

All besides B and D, because a cross section at vertices are nothing more than points, which is neither a polygon nor a disc.