Lemmara logoLemmaraWorked solution

0580/32 Oct/Nov 2024, Question 6: Nets of 3D Shapes

Cambridge IGCSE Mathematics 0580 · Paper 32 (Core) · Calculator · 10 marks

اقرأ هذا الحل مشروحاً بالعربي ←

The question, in short

Complete a cuboid net on a 1 cm² grid, find angle x where three regular pentagons meet, and use parallel-line angle facts to find x and y.

Summarised in our own words. Use the official paper for the exact wording and the diagram.

Part (a) · 3 marks

On the 1 cm² grid, draw the remaining faces to complete a net of the 4 cm by 4 cm by 2 cm cuboid, starting from the given 4 cm by 4 cm face.

  1. 1Faces needed: two 4 × 4 squares and four 4 × 2 rectangles
  2. 2Row: the given 4 × 4, then 4 × 2, 4 × 4, 4 × 2, joined along 4 cm edges
  3. 3Put a 4 × 2 rectangle on each of the other two sides of the given 4 × 4 face

AnswerFully correct net

Part (b) · 3 marks

Three regular pentagons meet at A; work out the size of the gap angle x between two of them.

  1. 1Interior angle of a regular pentagon = 180 − 360/5 = 108°
  2. 2x = 360 − 3 × 108
  3. 3= 36

Answer36

Part (ci) · 2 marks

Using the parallel lines and the 23° and 35° angles shown, find x and state a geometrical reason.

  1. 1The steeper line makes 35 + 23 = 58° with the upper parallel line
  2. 2x = 58
  3. 3Corresponding angles are equal

Answer58, Corresponding angles

Part (cii) · 2 marks

Using the same parallel-line diagram, find the value of y.

  1. 1The less steep line makes 35° with the lower parallel line (corresponding angles)
  2. 2y = 180 − 35 = 145 (angles on a straight line)

Answer145

Stuck on a step? Read the free lesson: Nets of 3D Shapes

Practise more nets of 3d shapes questions

Real 0580 past-paper questions, marked on your working like the exam, with a worked solution for every part.

Practise free on Lemmara

More past-paper questions on nets of 3d shapes

Also searched as: 0580/32/O/N/24 · 0580_w24_qp_32 · 0580 w24 32 · question 6.
Lemmara is an independent study tool, not affiliated with or endorsed by Cambridge International Education. The worked solutions are Lemmara’s own.