4MA0 Higher January 2012 Paper 4 Q20
20
Diagram NOT accurately drawn
A solid cone has a slant height of 9 cm.
The curved surface area of the cone is 100 cm\(^2\).
Calculate the volume of the cone.
Give your answer correct to 3 significant figures.
(5)
| Scheme | Marks |
|---|---|
| \(\pi \times r \times 9 = 100\) oe | M1 |
| (\(r\) =) 3.53677… | A1 |
| \(\sqrt{9^2 - \text{“}3.53...\text{”}^2}\) | M1 |
| (\(h\) =) 8.2759… | A1 |
| 108 | A1 |
| (Total 5 marks) |
Notes
A1: for 3.53
or for value rounding to 3.54
(3.14 → 3.53857…)
A1: for 8.27
or for value rounding to 8.28
A1: for answer rounding to 108
(\(\pi\) → 108.40…
3.14 → 108.45…)
If both M1s scored , award 5 marks for an answer which rounds to 108
Apart from Questions 3, 13(b) and 17(f) (where the mark scheme states otherwise), the correct answer, unless clearly obtained by an incorrect method, should be taken to imply a correct method.