Date | May 2010 | Marks available | 6 | Reference code | 10M.2.hl.TZ1.3 |
Level | HL only | Paper | 2 | Time zone | TZ1 |
Command term | Calculate | Question number | 3 | Adapted from | N/A |
Question
In the right circular cone below, O is the centre of the base which has radius 6 cm. The points B and C are on the circumference of the base of the cone. The height AO of the cone is 8 cm and the angle BˆOC is 60°.
Calculate the size of the angle BˆAC.
Markscheme
AC = AB = 10 (cm) A1
triangle OBC is equilateral (M1)
BC = 6 (cm) A1
EITHER
BˆAC=2arcsin310 M1A1
BˆAC=34.9∘(accept 0.609 radians) A1
OR
cosBˆAC=102+102−622×10×10=164200 M1A1
BˆAC=34.9∘(accept 0.609 radians) A1
Note: Other valid methods may be seen.
[6 marks]
Examiners report
The question was generally well answered, but some students attempted to find the length of arc BC.