Stage 9 - Q1 - 3 marks
A cuboid has three different side lengths 7, 9, 11 cm. State and describe all its planes of symmetry.
Hint
Consider a central cut parallel to each face direction.
Stage 9 - Q2 - 4 marks
A cube has side 11 cm. Count its planes of symmetry, separating the two families.
Hint
A cube has extra diagonal symmetries that a cuboid with unequal edges lacks.
Stage 9 - Q3 - 3 marks
A right prism has a regular 8-gon cross-section and length 8 cm. Count and describe its planes of symmetry.
Hint
Remember the plane halfway between the two ends.
Stage 9 - Q4 - 4 marks
A right square prism has base side 11 cm and length 14 cm. It is not a cube. Count its symmetry planes and explain why it has fewer than a cube.
Hint
Do not assume that every square prism is a cube.
Stage 9 - Q5 - 3 marks
A right circular cylinder has radius 7 cm and height 19 cm. Describe its planes of symmetry.
Hint
The circular cross-section has infinitely many diameter lines.
Stage 9 - Q6 - 4 marks
A right prism has an L-shaped cross-section: outer arms 4 cm and 3 cm, both of thickness 1 cm. Its length is 26 cm. Explain its number of symmetry planes.
Hint
Separate cross-section reflections from the central transverse plane.
Stage 9 - Q7 - 4 marks
A right square prism has base side 13 cm and length 16 cm. It is not a cube. Count its symmetry planes and explain why it has fewer than a cube.
Hint
Do not assume that every square prism is a cube.
Stage 9 - Q8 - 3 marks
A right prism has a regular 10-gon cross-section and length 13 cm. Count and describe its planes of symmetry.
Hint
Remember the plane halfway between the two ends.
Stage 9 - Q9 - 4 marks
A right prism has an L-shaped cross-section: outer arms 4 cm and 3 cm, both of thickness 1 cm. Its length is 8 cm. Explain its number of symmetry planes.
Hint
Separate cross-section reflections from the central transverse plane.
Stage 9 - Q10 - 6 marks
Classify the planes of symmetry of rectangular prisms with: (i) all three edge lengths different; (ii) exactly two equal; (iii) all three equal. Explain why the counts change, and give one numerical example for each case.
Hint
Start with the three planes that exist for every cuboid, then check the new reflections created by equal edges.