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Grade 7

10.03 Classify solids

Worksheet
3D shapes
1

Name the following solids:

a
b
c
2

For each of the following solids:

i

Name the solid.

ii

State whether the solid has a uniform cross-section.

iii

State the order of rotational symmetry about an vertical axis down the center of the solid.

iii

State whether the solid has plane symmetry.

a
b
c
d
e
f
g
h
3

Explain why shapes A and B are polyhedra while shape C is not.

4

Determine whether the following solids are polyhedrons:

a
b
c
d
5

State whether the following solids have faces, vertices and edges:

a

Sphere

b

Cone

c

Tetrahedron

d

Cylinder

6

Consider a rectangular prism.

a

How many faces meet at any one vertex?

b

How many faces meet at any one edge?

c

How many edges meet at any one vertex?

7

Consider the following hexagonal pyramid:

a

How many faces does it have?

b

How many vertices does it have?

c

How many edges does it have?

8

Complete the table with the number of features for each solid:

3D shapeNumber of facesNumber of verticesNumber of edges
\text{Hexagonal prism}
\text{Triangular pyramid}
\text{Rectangular prism}
9

Consider given the rectangular prism:

a

Name two parallel edges.

b

Name two edges that are both intersecting and perpendicular.

c

Name all of the edges that are parallel to B H.

d

Name all of the edges that are perpendicular to BH.

e

Does the prism have plane symmetry about the plane AFGB?

10

Consider the given hexagonal prism:

a

Name the face that is parallel to FEKL.

b

How many faces are perpendicular to ABCDEF?

c

Name two parallel edges.

d

Name two perpendicular edges.

e

State whether the following are planes of symmetry for the prism:

i
BEKH
ii
ADJG
iii
BDJH
iv
CFLI
11

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.

a

How many of the small cubes will have at least one face painted blue?

b

How many of the small cubes will have at least two faces painted blue?

c

How many of the small cubes will have three faces painted blue?

12

Euler related the number of faces, edges and vertices of any polyhedron in one formula.

a

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
b

Determine whether each of the following rules correctly states the relationship between the number of faces, vertices and edges of a polyhedron:

i
F + V - E = 2
ii
F + V + E = 2
iii
E + V - F = 2
iv
F + E - V = 2
13

Select the right name for each solid from the list below:

  • Square pyramid

  • Rectangular pyramid

  • Triangular prism

  • Rectangular prism

  • Octagonal pyramid

  • Octagonal prism

a
b
c
d
e
f
14

How many planes of symmetry do the following solids have?

a

Cube

b

Sphere

c

Cone

d

Square prism

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Outcomes

7.E1.1

Describe and classify cylinders, pyramids, and prisms according to their geometric properties, including plane and rotational symmetry.

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