Higher June 2024 Paper 1 Q21
21 A solid cuboid has a volume of 300 cm3
The cuboid has a total surface area of 370 cm2
The length of the cuboid is 20 cm.
The width of the cuboid is greater than the height of the cuboid.
Work out the height of the cuboid.
You must show all your working. (5)
| Answer | Mark | Mark scheme |
|---|---|---|
| 2.5 | P1 | for forming an equation using the volume, eg \(20wh = 300\) or \(wh = 15\) oe or for \(300 \div 20\ (= 15)\) |
| P1 | for forming an equation using the surface area, eg \(20w + 20w + 20h + 20h + hw + hw = 370\) oe or \(20w + 20w + 20h + 20h + 30 = 370\) oe | |
| P1 | for eliminating one variable, eg \(40h + \dfrac{600}{h} + 30 = 370\) or \(40h^2 - 340h + 600\ (= 0)\) or \(2h^2 - 17h + 30\ (= 0)\) | |
| P1 | for process to solve quadratic equation, eg \((2h - 5)(h - 6)\ (= 0)\) or \(\dfrac{17 \pm \sqrt{(-17)^2 - 4 \times 2 \times 30}}{2 \times 2}\) | |
| A1 | for 2.5 oe |
Additional guidance
Can use any variables for height and width
Use of 30 in this equation implies 1st P1
Award P4 for answer of 6 if 2.5 and 6 identified and supported by working that involves both volume and surface area
Do not award A1 for 2.5 if it is not supported by working that involves both volume and surface area