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Grade 3 · Foundation · free GCSE maths worksheet

Nets and properties of 3D shapes

Faces, edges, vertices and drawing nets.

17 original questions, 41 marks. Print the worksheet, mark it with the answers sheet, and use the solutions to see every step written out by hand.

Worksheet PDFWorked solutions PDFAnswers PDF

The questions

1

A net folds to make a triangular prism.

How many triangles and how many rectangles are in the net?

2 marks
Show answer
triangles) 2 rectangles) 3
2

A net is made from one square and four identical triangles.

Write down the name of the solid it folds to make.

2 marks
Show answer
square-based pyramid
3
  1. Write down the number of faces of a cube.
  2. Write down the number of vertices of a cube.
2 marks
Show answer
a) 6 b) 8
4

A net is made from two circles and one rectangle.

Write down the name of the solid it folds to make.

2 marks
Show answer
cylinder
5

A 3D solid has exactly one square face and four triangular faces.

  1. Write down the mathematical name of this solid.
  2. Write down the number of edges of this solid.
2 marks
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a) square-based pyramid b) 8
6

A cube has sides of length 4 cm.

Work out the total area of the net of the cube.

2 marks
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96 cm2
7

Here is a triangular prism.

  1. Write down the number of faces of a triangular prism.
  2. Write down the number of edges of a triangular prism.
2 marks
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a) 5 b) 9
8

Sam draws a net made of 5 identical squares and says it will fold to make a cube.

Is Sam right? Give a reason.

2 marks
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No, a cube has 6 faces
9
  1. A 3D solid has one curved surface, no edges and no vertices. Write down the mathematical name of this solid.
  2. A different 3D solid has two flat circular faces and one curved surface. Write down the mathematical name of this solid.
2 marks
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a) sphere b) cylinder
10

A cuboid measures 5 cm by 3 cm by 2 cm.

Work out the total area of the net of the cuboid.

3 marks
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62 cm2
11
  1. A 3D solid has exactly one circular face and one vertex. Write down the mathematical name of this solid.
  2. In the space below, draw a sketch of a cuboid.
2 marks
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a) cone b) any recognisable 3D sketch of a cuboid
12

The diagram shows the net of a cube. It is made from 6 identical squares.

The net is folded to make the cube.

  1. The face marked X is the bottom of the cube. Shade the face that is the top of the cube.
  2. Write down the size of angle p.
  3. Write down the number of edges of the cube.
Xp
3 marks
Show answer
a) The square above the second square of the row (opposite X) b) 90° c) 12
13

A prism has 9 edges.

  1. What shape is the cross-section of the prism?
  2. How many faces does the prism have?
3 marks
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a) triangle b) 5
14

A prism has a cross-section that is a pentagon.

  1. Write down the number of faces of the prism.
  2. Write down the number of edges of the prism.
  3. Write down the number of vertices of the prism.
3 marks
Show answer
a) 7 b) 15 c) 10
15

A prism has a cross-section that is an equilateral triangle with sides of length 4 cm.

The length of the prism is 9 cm.

Work out the total length of all the edges of the prism.

4 cm9 cm4 cmCross-section is an equilateral triangle
3 marks
Show answer
51 cm
16

A prism has a cross-section that is a regular octagon with sides of length 3 cm.

The length of the prism is 10 cm.

  1. Write down the number of edges of the prism.
  2. Work out the total length of all the edges of the prism.
3 cm10 cmDiagram NOT accurately drawn
3 marks
Show answer
a) 24 b) 128 cm
17

The ends of a triangular prism are right-angled triangles with sides 3 cm, 4 cm and 5 cm.

The prism is 10 cm long.

Work out the total area of the net of the prism.

3 marks
Show answer
132 cm2

Every question here is original and written by Robinson Tuition. The grade follows the Edexcel grade descriptors and suits AQA and OCR too; this is not an exam-board paper.

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