Geometry of 3-D Objects: Faces, Vertices, Edges & Nets — Worksheet & Memo

∑ DANEMATHICS

FREE CAPS MATHS RESOURCES

Grade 9 · Geometry of 3-D Objects

Geometry of 3-D Objects: Faces, Vertices, Edges & Nets

EXAM-STYLE CLASS TEST

Marks

Duration

55 minutes

Questions

Name:

Class:

Date:

Mark

/ 34

Instructions and Information

Answer ALL the questions in this question paper.
Answer QUESTION 1 by circling the letter (A–D) in the answer grid at the end of that section.
Show ALL calculations clearly.
Show all units where applicable.
Number the answers correctly according to the numbering system used in this question paper.
A non-programmable calculator may be used, unless stated otherwise.
Write neatly and legibly.

Question 1

[10 MARKS]

Four options are given as possible answers to the following questions. Choose the correct answer and circle the letter (A–D) in the grid at the end of this section. If you want to change your choice, put a cross through the wrong letter and circle your new choice.

1.1
Euler's formula for a polyhedron is …
(1)
A)F + V + E = 2
B)F + V − E = 2
C)F − V + E = 2
D)F × V ÷ E = 2
1.2
A tetrahedron has 4 faces and 4 vertices. Its number of EDGES is …
(1)
A)8
B)6
C)4
D)12
1.3
A prism with a hexagonal cross-section has … faces.
(1)
A)6
B)8
C)12
D)7
1.4
The difference between a prism and a pyramid is that a pyramid has …
(1)
A)two identical parallel bases
B)ONE base and triangular faces meeting at an apex
C)only curved surfaces
D)no vertices
1.5
Which solid has NO vertices at all?
(1)
A)cube
B)sphere
C)cone
D)square pyramid
1.6
A net of a cube consists of …
(1)
A)4 squares
B)6 squares
C)8 squares
D)6 rectangles
1.7
Euler's formula does NOT apply to a cylinder because a cylinder …
(1)
A)has too many faces
B)has a CURVED surface
C)has no edges
D)is too large
1.8
An octahedron has 8 faces and 12 edges. Its number of VERTICES is …
(1)
A)4
B)6
C)8
D)20
1.9
Which one of the following is NOT a Platonic solid?
(1)
A)cube
B)square pyramid
C)tetrahedron
D)octahedron
1.10
A cube has 6 faces, 8 vertices and 12 edges. Euler's formula gives …
(1)
A)26
B)2
C)10
D)14

Answer grid — circle your answers for Question 1

1.1	A	B	C	D
1.2	A	B	C	D
1.3	A	B	C	D
1.4	A	B	C	D
1.5	A	B	C	D
1.6	A	B	C	D
1.7	A	B	C	D
1.8	A	B	C	D
1.9	A	B	C	D
1.10	A	B	C	D

Question 2

[12 MARKS]

The solid below is a cube.

2.1
Write down the number of faces, vertices and edges.
(3)
2.2
Verify Euler's formula for this solid, and hence determine how many edges a solid with 5 faces and 6 vertices must have.
(3)
2.3
A different solid has 5 faces and 6 vertices. Use Euler's formula to find its number of edges, and name the solid.
(3)
2.4
Explain why Euler's formula cannot be applied to a cylinder, and name the part of a cylinder that prevents it.
(3)

Question 3

[12 MARKS]

Answer the questions below about 3-D objects. F is the number of faces, V the number of vertices and E the number of edges.

3.1
A tetrahedron has 4 faces and 4 vertices. Use Euler's formula to determine its number of edges.
(3)
3.2
An octahedron has 8 faces, 6 vertices and 12 edges. Verify Euler's formula for it, and hence determine how many edges meet at each vertex.
(3)
3.3
A prism has a hexagonal cross-section. Determine its number of faces, vertices and edges.
(4)
3.4
Explain the difference between a prism and a pyramid.
(2)

TOTAL: 34 marks

This question paper consists of 3 questions.