Symmetry of solids

Sample Symmetry of solids questions

A few of the 20 questions, from easier to harder. Choose your exam board and tier to practise them, with every answer marked.

1. Question 11 markGrade 4
   A cuboid has a square base of side 6 cm and a height of 10 cm. The shaded plane is vertical and halfway between two opposite faces. Is the shaded plane a plane of symmetry of the solid? [1]
   Show the worked solution

   The plane cuts the cuboid into two identical halves that are mirror images of each other, so it is a plane of symmetry. B1
2. Question 21 markGrade 5
   A solid cone has a circular base and its apex is directly above the centre of the base. How many axes of symmetry does the cone have? [1]
   Show the worked solution

   The only line the cone can be turned about and still look the same is the line from the apex to the centre of the base. So it has 1 axis of symmetry. B1
3. Question 31 markGrade 5
   A cone has a base radius of 3 cm and a height of 8 cm. Its apex is directly above the centre of the base. The shaded plane passes through the apex and the centre of the base. Is the shaded plane a plane of symmetry of the solid? [1]
4. Question 41 markGrade 6
   A cube. Write down the number of planes of symmetry of the cube. [1]
5. Question 52 marksGrade 6
   A regular hexagonal prism has two hexagonal faces and six identical rectangular faces. (a) Write down the number of planes of symmetry of the solid. [1] (b) Write down the order of rotational symmetry of the solid about the axis through the centres of its two hexagonal faces. [1]
6. Question 61 markGrade 7
   A cuboid has a rectangular base measuring 4 cm by 8 cm and a height of 10 cm. The shaded plane is vertical and passes through two opposite vertical edges. Is the shaded plane a plane of symmetry of the solid? [1]

Common mistakes in Symmetry of solids

When a pupil makes one of these on Revision Workshop, the marking engine names the mistake and explains it, instead of just marking the answer wrong.

• Planes of symmetry equals rotational order

  Gave the order of rotational symmetry as the number of planes of symmetry. For this solid they are different: count the mirror planes separately (there are 2 planes through opposite edges' midpoints of the square, 2 diagonal planes, and 1 horizontal plane halfway up: 2 + 2 + 1).

• Counts diameter as axis

  The only axis of rotational symmetry is the line from the apex to the centre of the base.

• Counts faces not planes

  Counted the 6 faces. A cube has 3 planes parallel to pairs of faces and 6 diagonal planes through opposite edges: 3 + 6 = 9.