Name the following solids:
For each of the following solids:
Name the solid.
State whether the solid has a uniform cross-section.
Explain why shapes A and B are polyhedra while shape C is not.
Select the right name for each solid from the list below:
-
Square pyramid
Rectangular pyramid
-
Triangular prism
Rectangular prism
-
Octagonal pyramid
Octagonal prism
State whether the following solids have faces, vertices and edges:
Sphere
Cone
Tetrahedron
Cylinder
Consider the following hexagonal pyramid:
How many faces does it have?
How many vertices does it have?
How many edges does it have?
Determine whether the following solids are polyhedrons:
Consider a rectangular prism.
How many faces meet at any one vertex?
How many faces meet at any one edge?
How many edges meet at any one vertex?
Complete the table with the number of features for each solid:
| 3D shape | Number of faces | Number of vertices | Number of edges |
|---|---|---|---|
| \text{Hexagonal prism} | |||
| \text{Triangular pyramid} | |||
| \text{Rectangular prism} |
Consider given the rectangular prism:
Name two skew edges.
Name two parallel edges.
Name two edges that are both intersecting and perpendicular.
Name all of the edges that are parallel to B H.
Name all of the edges that are perpendicular to BH.
Consider the given hexagonal prism:
Name the face that is parallel to FEKL.
How many faces are perpendicular to ABCDEF?
Name two skew edges.
Name two parallel edges.
Name two perpendicular edges.
A number of 1\text{ cm} \times 1\text{ cm} \times 1\text{ cm} cubes are glued together to form a \\ 3\text{ cm} \times 3\text{ cm} \times 3\text{ cm} cube as shown:
The outside faces of the large cube are painted blue and the small cubes are then pulled apart.
How many of the small cubes will have at least one face painted blue?
How many of the small cubes will have at least two faces painted blue?
How many of the small cubes will have three faces painted blue?
Euler related the number of faces, edges and vertices of any polyhedron in one formula.
Complete:
| \text{Solid} | \text{Number } \\ \text{of Faces (F)} | \text{Number } \\ \text{of Vertices (V)} | \text{Number } \\ \text{of Edges (E)} | F+V |
| \text{Rectangular Prism} | 8 | |||
| \text{Triangular Prism} | 6 | |||
| \text{Hexagonal Prism} | 12 | |||
| \text{Triangular Pyramid} | 4 | |||
| \text{Pentagonal Pyramid} | 6 |
Hence determine Euler's rule for the relationship between the number of faces, vertices and edges of a polyhedron.