| Date | May 2017 | Marks available | 4 | Reference code | 17M.1.sl.TZ2.3 |
| Level | SL only | Paper | 1 | Time zone | TZ2 |
| Command term | Give your answer and Find | Question number | 3 | Adapted from | N/A |
Question
A lampshade, in the shape of a cone, has a wireframe consisting of a circular ring and four straight pieces of equal length, attached to the ring at points A, B, C and D.
The ring has its centre at point O and its radius is 20 centimetres. The straight pieces meet at point V, which is vertically above O, and the angle they make with the base of the lampshade is 60°.
This information is shown in the following diagram.
Find the length of one of the straight pieces in the wireframe.
Find the total length of wire needed to construct this wireframe. Give your answer in centimetres correct to the nearest millimetre.
Markscheme
\(\cos 60^\circ = \frac{{20}}{b}\)\(\,\,\,\)OR\(\,\,\,\)\(b = \frac{{20}}{{\cos 60^\circ }}\) (M1)
Note: Award (M1) for correct substitution into a correct trig. ratio.
\((b = ){\text{ 40 (cm)}}\) (A1) (C2)
[2 marks]
\(4 \times 40 + 2\pi (20)\) (M1)(M1)
Note: Award (M1) for correct substitution in the circumference of the circle formula, (M1) for adding 4 times their answer to part (a) to their circumference of the circle.
285.6637… (A1)(ft)
Note: Follow through from part (a). This (A1) may be implied by a correct rounded answer.
285.7 (cm) (A1)(ft) (C4)
Notes: Award (A1)(ft) for rounding their answer (consistent with their method) to the nearest millimetre, irrespective of unrounded answer seen.
The final (A1)(ft) is not dependent on any of the previous M marks. It is for rounding their unrounded answer correctly.
[4 marks]
