4400 Higher June 2010 Paper 4 Q19
19 A cone has slant height 4 cm and base radius \(r\) cm.
Diagram NOT accurately drawn
The total surface area of the cone is \(\dfrac{33}{4}\pi\) cm2.
Calculate the value of \(r\).
(4)
| Scheme | Marks |
|---|---|
| \(\pi r \times 4 + \pi r^2 = \frac{33}{4}\pi\) oe | M1 |
| \(r^2 + 4r - \frac{33}{4} = 0\) oe \((4r^2 + 16r - 33 = 0)\) | M1 |
| \((2r - 3)(2r + 11) = 0\) | M1 |
| 1.5 | A1 |
| (4) | |
| (4 marks) |
Notes
M1: ie correct equation based on areas.
M1: correct equation = 0
M1: \(\dfrac{-4 \pm \sqrt{4^2 + 4 \times \frac{33}{4}}}{2}\) or \(\dfrac{-16 \pm \sqrt{16^2 + 16 \times 33}}{8}\)
A1: not “1.5 and/or \(-\frac{11}{2}\)” unless 1.5 clearly chosen
A1 dependent on M3