Higher November 2020 Paper 2 Q18
18 The diagram shows cuboid \(ABCDEFGH\).
Diagram NOT accurately drawn
\(AB = 5\) cm
\(AH = 4\) cm
The size of the angle between \(CH\) and the plane \(ABCD\) is 35°
Calculate the volume of the cuboid.
Give your answer correct to 3 significant figures.
(5)
| Scheme | Marks |
|---|---|
eg \(\dfrac{4}{AC} = \tan 35\) oe or \(\dfrac{AC}{4} = \tan 55\) oe or \(\dfrac{AC}{\sin 55} = \dfrac{4}{\sin 35}\) oe or \(CH = \dfrac{4}{\sin 35}\) oe (= 6.97...) and \(\dfrac{AC}{\text{“}6.97\text{”}} = \cos 35\) oe or \(CH = \dfrac{4}{\sin 35}\) oe (=6.97...) and \(AC^2 = 6.97^2 - 4^2\) oe | M1 |
\((AC =)\; \dfrac{4}{\tan 35}\) oe eg \((AC =)\) 4tan55 (= 5.71...) or \((AC =)\; \dfrac{4\sin 55}{\sin 35}\) or “6.97” × cos35 oe or \((AC =)\; \sqrt{\text{“}6.97\text{”}^2 - 4^2}\) | M1 |
| \((BC =)\; \sqrt{\text{“}5.71\text{”}^2 - 5^2}\) (= 2.76...) | M1 |
| 4 × 5 × “2.76...” | M1 |
| Correct answer scores full marks (unless from obvious incorrect working) Answer: 55.3 | A1 |
| (5) | |
| (5 marks) |
Notes
M1: A correct trig statement involving \(AC\) or trig and then Pythagoras involving \(AC\)
M1: complete method to find \(AC\)
M1: complete method to find \(BC\)
M1: method to find volume
A1: accept 55.1 – 55.5