Higher November 2018 Paper 3 Q8
8 The diagram shows a solid metal cuboid.
The areas of three of the faces are marked on the diagram.
The lengths, in cm, of the edges of the cuboid are whole numbers.
The metal cuboid is melted and made into cubes.
Each of the cubes has sides of length 2.5 cm.
Work out the greatest number of these cubes that can be made. (5)
| Answer | Mark | Mark scheme |
|---|---|---|
| 8 | P1 | process to start the problem eg \(xy = 45\) and \(xz = 15\) and \(yz = 27\) or \(5 \times 9\) (=45) and \(3 \times 9\) (=27) and \(3 \times 5\) (=15) or 3, 5 and 9 stated |
| P1 | for \(3 \times 5 \times 9\) (=135) or 2 of \(\text{``}9\text{''} \div 2.5\) (=3.6) or \(\text{``}5\text{''} \div 2.5\) (=2) or \(\text{``}3\text{''} \div 2.5\) (=1.2) | |
| P1 | for \(2.5^3\) (=15.625) or all of \(\text{``}9\text{''} \div 2.5\) (=3.6) and \(\text{``}5\text{''} \div 2.5\) (=2) and \(\text{``}3\text{''} \div 2.5\) (=1.2) | |
| P1 | for a complete process to find the number of cubes possible eg [volume] \(\div\ \text{``}15.625\text{''}\) (=8.64) or \(\text{``}3.6\text{''} \times \text{``}2\text{''} \times \text{``}1.2\text{''}\) (=8.64) | |
| A1 | cao |
Additional guidance
Maybe seen on diagram
[Volume] must come from multiplying together what they clearly indicate as the 3 dimensions of the cuboid. The three dimensions cannot be 45, 27 and 15