Foundation June 2023 Unit 2 Q17
17. A solid metal cuboid has dimensions 4 cm, 5 cm and 20 cm.
Diagram not drawn to scale
The cuboid is melted down. The metal is used to make solid cubes, each with sides 3 cm.
How many complete cubes will be made?
You must show all your working. [5]
| Scheme | Marks | Comments |
|---|---|---|
| (Volume of cuboid = 4 × 5 × 20 =) 400 (cm3) | B1 | Award B0 if 400 has come from incorrect working or if subsequent working is seen (e.g. finding the total surface area or 4 × 5 × 20 = 400, 400 × 2 = 800). |
| (Volume of cube = 3 × 3 × 3 =) 27 (cm3) | B1 | |
| (Number of cubes = ) \(\dfrac{4 \times 5 \times 20}{3 \times 3 \times 3}\) or equivalent | M1 | FT ‘their 400’ ÷ ‘their 27’, provided ‘their 27’ ≠ 3 and that B1 has previously been awarded or 4 × 5 × 20 and 3 × 3 × 3 seen. |
| = 14·8(…..) | A1 | May be implied in the final answer. |
| (Number of complete cubes = ) 14 | B1 | FT only if truncation required. If \(\dfrac{4 \times 5 \times 20}{3 \times 3 \times 3}\) = 14 (complete cubes) is seen, then award B1 B1 M1 A1 B1. |