Nets and 3D Shape Reasoning - Worksheets, Questions and Revision

14 original exam-style questions - 4 pages of questions with a full mark scheme - free printable PDF.

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11+ · Geometry

EP.M120 Nets and 3D Shape Reasoning

GL ASSESSMENT GL-11PLUS-MATHS · Calculators not allowed · about 55 minutes
Total Marks
Name: _______________________________    Date: ____ / ____ / ______
Answer ALL questions. Show all your working.
1
Which of the following nets will fold to make a triangular prism?
  • A) Two triangles separated by a gap, and three rectangles attached end-to-end in a row not touching the triangles
  • B) Two equal triangles attached to opposite ends of a straight strip of three rectangles so each triangle meets one rectangle along a full side
  • C) Two equal triangles joined along one edge with three rectangles attached around the other sides of the joined triangles
  • D) One triangle and four rectangles arranged in a cross so that only one rectangle touches the triangle
  • E) Three triangles in a row with three rectangles attached to the middle triangle only
(Total for Question 1 is 1 mark)
2
Which of these nets cannot fold to make a cube?
  • A) A row of four squares with one square attached above the second square and one square attached below the second square
  • B) A cross shape: one central square with four squares attached to each side and one added to one of those side squares
  • C) Two separate groups of three squares not connected to each other
  • D) A column of four squares with one square attached to the left of the second square and one square attached to the right of the second square
  • E) A row of four squares with one square attached above the third square and one square attached below the third square
(Total for Question 2 is 1 mark)
3
A net shows six rectangles where opposite rectangles are different sizes (two small, two medium, two large). Which solid could this net make?
  • A) Cube
  • B) Cuboid (rectangular prism)
  • C) Square-based pyramid
  • D) Triangular prism
  • E) Tetrahedron
(Total for Question 3 is 1 mark)
4
How many faces does a square-based pyramid have?
  • A) 3
  • B) 4
  • C) 5
  • D) 6
  • E) 8
(Total for Question 4 is 1 mark)
5
How many edges does a triangular prism have?
  • A) 6
  • B) 7
  • C) 8
  • D) 9
  • E) 10
(Total for Question 5 is 1 mark)
6
A regular tetrahedron (triangular pyramid with all equal faces) has how many vertices?
  • A) 3
  • B) 4
  • C) 5
  • D) 6
  • E) 8
(Total for Question 6 is 1 mark)
7
Which net will fold to make a cube if the faces are labelled so that face 1 is opposite face 6? (Descriptions only.)
  • A) Six squares in a straight row labelled 1 to 6
  • B) A cross with central square 3, squares 1 and 5 attached opposite sides and 2 attached above and 4 below central square, 6 attached to the right of square 5
  • C) A 2x3 rectangle of squares labelled 1 to 6 left-to-right top row then bottom row
  • D) A row of four squares labelled 2, 1, 4, 6 from left to right, with a square labelled 3 attached above the second square (labelled 1) and a square labelled 5 attached below the second square (labelled 1)
  • E) Two L-shaped groups of three squares joined at one corner
(Total for Question 7 is 1 mark)
8
A net shows two equilateral triangles and three rectangles arranged so that the two triangles are attached to the opposite ends of the strip of three rectangles. It folds to make a solid.
Name the solid. Then give the number of faces, edges and vertices.
(Total for Question 8 is 3 marks)
9
Consider this net: six equal squares in a straight row labelled 1 to 6. Can this net fold to make a cube? Give your answer and a brief reason.
(Total for Question 9 is 2 marks)
10
A cuboid has dimensions 2 cm by 3 cm by 4 cm. Work out its total surface area in square centimetres.
(Total for Question 10 is 3 marks)
11
A triangular prism has 5 faces and 9 edges. Use Euler's formula V - E + F = 2 to find the number of vertices V.
(Total for Question 11 is 2 marks)
12
A polyhedron has 8 vertices and 12 edges. Use Euler's formula to work out how many faces it has.
(Total for Question 12 is 3 marks)
13
A cuboid measures 2 cm by 3 cm by 6 cm. Calculate its total surface area. Then state how many faces, edges and vertices the cuboid has.
(Total for Question 13 is 4 marks)
14
A polyhedron has 10 faces and 16 vertices. Use Euler's formula to find the number of edges.
(Total for Question 14 is 4 marks)
Mark scheme · EP.M120 Nets and 3D Shape Reasoning

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Question 11

Question 12

Question 13

Question 14