3D solids, plans and elevations Worked Solutions — GCSE Maths

Fully worked, step-by-step solutions to GCSE 3D solids, plans and elevations questions. See exactly how to solve problems on faces, edges and vertices, properties of 3D solids, naming 3D solids, prisms.

faces, edges and verticesproperties of 3D solidsnaming 3D solidsprismspyramidsEuler formula

GCSE Foundation70 questionsStep-by-step solutions

Question 1

1 markeasy

Work out the number of faces of a cube.

Worked solution

Picture the solid and decide what its faces are.
$\text{cube}$
A face is a flat surface, an edge is where two faces meet and a vertex is a corner where edges meet. Counting them carefully beats guessing.
Count the faces.
$\text{faces} = 4 + 2 = 6$
A prism has one face for each side of its cross-section, so $4$ rectangles round the outside, plus the two $4$ -sided ends: $6$ faces.
State the number of faces.
$\text{faces} = 6$
The solid has $6$ faces.

Answer

\text{faces} = 6

Question 2

2 markseasy

Work out the number of edges of a triangular prism.

Worked solution

Picture the solid and decide what its edges are.
$\text{triangular prism}$
A face is a flat surface, an edge is where two faces meet and a vertex is a corner where edges meet. Counting them carefully beats guessing.
Count the vertices.
$\text{vertices} = 2 \times 3 = 6$
Each end of the prism is a polygon with $3$ corners, and there are two ends, so there are $6$ vertices.
State the number of edges.
$\text{edges} = 9$
The solid has $9$ edges.

Answer

\text{edges} = 9

Question 3

2 markseasy

Work out the number of vertices of a square-based pyramid.

Worked solution

Picture the solid and decide what its vertices are.
$\text{square based pyramid}$
A face is a flat surface, an edge is where two faces meet and a vertex is a corner where edges meet. Counting them carefully beats guessing.
Count the edges.
$\text{edges} = 2 \times 4 = 8$
There are $4$ edges round the base and $4$ sloping edges up to the apex, giving $8$ edges.
State the number of vertices.
$\text{vertices} = 5$
The solid has $5$ vertices.

Answer

\text{vertices} = 5

Question 4

2 markseasy

Work out the number of faces of a hexagonal prism.

Worked solution

Picture the solid and decide what its faces are.
$\text{hexagonal prism}$
A face is a flat surface, an edge is where two faces meet and a vertex is a corner where edges meet. Counting them carefully beats guessing.
Count the faces.
$\text{faces} = 6 + 2 = 8$
A prism has one face for each side of its cross-section, so $6$ rectangles round the outside, plus the two $6$ -sided ends: $8$ faces.
State the number of faces.
$\text{faces} = 8$
The solid has $8$ faces.

Answer

\text{faces} = 8

Question 5

1 markeasy

Work out the number of vertices of a cuboid.

Worked solution

Picture the solid and decide what its vertices are.
$\text{cuboid}$
A face is a flat surface, an edge is where two faces meet and a vertex is a corner where edges meet. Counting them carefully beats guessing.
Count the edges.
$\text{edges} = 3 \times 4 = 12$
There are $4$ edges round each end and $4$ edges joining the two ends, giving $2 \times 4 + 4 = 12$ edges.
State the number of vertices.
$\text{vertices} = 8$
The solid has $8$ vertices.

Answer

\text{vertices} = 8

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