4MA0 Higher January 2014 Paper 4R Q21
21
Diagram NOT accurately drawn
The diagram shows a solid cone.
The base of the cone is a horizontal circle, centre \(O\), with radius 4.5 cm.
\(AB\) is a diameter of the base and \(OV\) is the vertical height of the cone.
The curved surface area of the cone is 130 cm2
Calculate the size of the angle \(AVB\).
Give your answer correct to 1 decimal place.
(4)
| Scheme | Marks |
|---|---|
| \(130 = \pi \times 4.5 \times l\) | M1 |
| \(l = \dfrac{130}{4.5\pi}\) or \(l = 9.1956\) | M1 |
| \(\sin(AVO) = 4.5/\text{“}9.20\text{”}\) (= 0.489..) | M1 |
| 58.6 | A1 |
| (4) | |
| (4 marks) |
Notes
M1: For exact expression or answer which rounds to 9.2
M1: For a correct expression for sin \(AVO\) or cos AVB
\(\cos(AVB) = (\text{“}9.2\text{”}^2 + \text{“}9.2\text{”}^2 - 9) / 2 \times \text{“}9.2\text{”} \times \text{“}9.2\text{”}\) (=0.521...)
A1: awrt 58.6