3-D shapes (Cross-sections, Vertices, Edges)：練習問題

If a square pyramid is cut by a plane parallel to its base, what is the shape of the resulting cross-section?

A certain pyramid has exactly \(14\) edges. How many vertices does this pyramid have?

A specific prism and a specific pyramid have exactly the same number of faces. If the sum of the total number of edges of the prism and the total number of edges of the pyramid is exactly \(32\), how many vertices does this pyramid have?

Which 3-D shape has exactly one flat circular base and one curved surface that meets at a sharp point?

A specific pyramid has exactly \(9\) faces. How many edges does this pyramid have?

How many vertices does a sphere have?

A hexagonal prism and a hexagonal pyramid both have bases of the same size and the same height. If a cross-section parallel to the base is taken for each shape exactly halfway up its height, which shape will have the larger cross-section, and why?

A certain prism has exactly \(18\) edges. A specific pyramid has the same number of vertices as this prism. How many faces does this pyramid have?

A triangular prism is a common 3-D shape found in geometry.
(a) How many faces does a triangular prism have in total?
(b) How many edges does it have?
(c) How many vertices does it have?
(d) What is the 2-D shape of its two bases?

An octagonal prism has a base that is an octagon (an 8-sided polygon).
(a) Calculate the total number of vertices of this prism.
(b) Calculate the total number of edges of this prism.
(c) Determine the total number of faces of this prism.
(d) If we cut the prism with a flat plane that is parallel to the base, what is the 2-D shape of the resulting cross-section?
(e) Is the size and shape of this cross-section the same as the base?