4MA0 Higher January 2015 Paper 3 Q21
21
Diagram NOT accurately drawn
A solid cone has a height of 15 cm.
The volume of the cone is \(320\pi\) cm3
Work out the curved surface area of the cone.
Give your answer correct to 3 significant figures.
(5)
| Scheme | Marks |
|---|---|
| \(\dfrac{1}{3}\pi r^2 \times 15 = 320\pi\) | M1 |
\((r =)\sqrt{\dfrac{3 \times 320\pi}{15\pi}}\) or \((r =)\sqrt{\dfrac{320}{5}}\) or \((r =)\sqrt{64}\) or \((r =)\ 8\) | M1 |
| \(l = \sqrt{15^2 + \text{“}8\text{”}^2}\) or \(l = 17\) | M1 |
| \(S = \pi \times \text{“}8\text{”} \times \sqrt{15^2 + \text{“}8\text{”}^2}\) or \(S = \pi \times 8 \times \text{“}17\text{”}\) | M1 |
| 427 | A1 |
| (5 marks) |
Notes
M1: For any correct expression for \(r\)
M1: dep on M2
M1: ft for \(r\) and \(l\) if all M marks scored.
Allow M1 for
\(\pi \times \text{“}8\text{”} \times \sqrt{15^2 + \text{“}8\text{”}^2} + \pi \times \text{“}8\text{”}^2\)
A1: for awrt 427
Accept \(136\pi\)