12.13 Visualising solids
Name the following solids:
Name the solid formed from each of the following nets:
Draw a net for the following solids:
Name the 3D shapes formed by the following nets:
State the solid that can be formed from the given sets of 2D shapes:
For each of the following solids formed from cubes:
Draw the diagram for the side view.
Draw the diagram for the front view.
Draw the diagram for the plan view.
Select the solid that matches the given elevations:
Name the following solids:
For each of the following solids:
Name the solid.
State whether the solid has a uniform cross-section.
State the order of rotational symmetry about an vertical axis down the center of the solid.
State whether the solid has plane symmetry.
Explain why shapes A and B are polyhedra while shape C is not.
Determine whether the following solids are polyhedrons:
State whether the following solids have faces, vertices and edges:
Sphere
Cone
Tetrahedron
Cylinder
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?
Consider the following hexagonal pyramid:
How many faces does it have?
How many vertices does it have?
How many edges does it have?
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 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.
Does the prism have plane symmetry about the plane AFGB?
Consider the given hexagonal prism:
Name the face that is parallel to FEKL.
How many faces are perpendicular to ABCDEF?
Name two parallel edges.
Name two perpendicular edges.
State whether the following are planes of symmetry for the prism:
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 |
Determine whether each of the following rules correctly states the relationship between the number of faces, vertices and edges of a polyhedron:
Select the right name for each solid from the list below:
-
Square pyramid
Rectangular pyramid
-
Triangular prism
Rectangular prism
-
Octagonal pyramid
Octagonal prism
How many planes of symmetry do the following solids have?
Cube
Sphere
Cone
Square prism