Lemmara logoLemmaraWorked solution

0580/31 Oct/Nov 2023, Question 4: Equating Volumes: Melting and Recasting

Cambridge IGCSE Mathematics 0580 · Paper 31 (Core) · Calculator · 9 marks

اقرأ هذا الحل مشروحاً بالعربي ←

The question, in short

Complete a net for a 5 cm by 3 cm by 2 cm cuboid on a 1 cm² grid, find its surface area, then use equal volumes of a 6 cm cube and a triangular prism to find x.

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

Part (ai) · 3 marks

On the 1 cm² grid, draw the remaining faces to complete the net of the 5 cm by 3 cm by 2 cm cuboid, starting from the given 5 cm by 3 cm face.

  1. 1The net needs 6 faces: two 5 × 3, two 5 × 2 and two 3 × 2 rectangles
  2. 2Attach 5 × 2 rectangles to the long (5 cm) sides and 3 × 2 rectangles to the short (3 cm) sides of the drawn face
  3. 3Attach the second 5 × 3 face to the far side of one 5 × 2 rectangle

AnswerFully correct net

Part (aii) · 2 marks

Calculate the total surface area of the cuboid with dimensions 5 cm, 3 cm and 2 cm.

  1. 12 × (5 × 2 + 3 × 2 + 5 × 3) = 2 × (10 + 6 + 15)
  2. 2= 62 cm²

Answer62

Part (b) · 4 marks

A cube of edge 6 cm and a right-angled triangular prism with legs 4 cm and x cm and length 9 cm have equal volumes; find x.

  1. 1Cube volume = 6³ = 216 cm³
  2. 2Prism volume = 1/2 × 4 × x × 9 = 18x
  3. 318x = 216
  4. 4x = 216 ÷ 18 = 12

Answer12

Stuck on a step? Read the free lesson: Equating Volumes: Melting and Recasting

Practise more equating volumes: melting and recasting 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 equating volumes: melting and recasting

Also searched as: 0580/31/O/N/23 · 0580_w23_qp_31 · 0580 w23 31 · question 4.
Lemmara is an independent study tool, not affiliated with or endorsed by Cambridge International Education. The worked solutions are Lemmara’s own.