4MA1/2F Jan 2022, Question 12: Volume of a Prism
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2F (Foundation) · Calculator · 5 marks
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The question, in short
Using the cuboid box B measuring 60 cm by 20 cm by 24 cm and 8 cm cube cartons C, find the volume of unused space left after packing as many cartons as possible.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Solution · 5 marks
- 160 ÷ 8 = 7.5, so 7 cartons fit along the length
- 220 ÷ 8 = 2.5, so 2 cartons fit along the width
- 324 ÷ 8 = 3, so 3 cartons fit along the height
- 47 × 2 × 3 = 42 cartons can fit in the box
- 5Volume of one carton = 8 × 8 × 8 = 512 cm³
- 6Total volume of cartons = 42 × 512 = 21504 cm³
- 7Volume of box = 60 × 24 × 20 = 28800 cm³
- 8Volume of packing material = 28800 − 21504 = 7296 cm³
Answer7296
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