Date | November 2017 | Marks available | 4 | Reference code | 17N.2.hl.TZ0.3 |
Level | HL only | Paper | 2 | Time zone | TZ0 |
Command term | Find | Question number | 3 | Adapted from | N/A |
Question
This diagram shows a metallic pendant made out of four equal sectors of a larger circle of radius OB=9 cmOB=9 cm and four equal sectors of a smaller circle of radius OA=3 cm.
The angle BOC= 20°.
Find the area of the pendant.
Markscheme
METHOD 1
area = (four sector areas radius 9) + (four sector areas radius 3) (M1)
=4(1292π9)+4(12327π18) (A1)(A1)
=18π+7π
=25π (=78.5 cm2) A1
METHOD 2
area =
(area of circle radius 3) + (four sector areas radius 9) – (four sector areas radius 3) (M1)
π32+4(1292π9)−4(1232π9) (A1)(A1)
Note: Award A1 for the second term and A1 for the third term.
=9π+18π−2π
=25π (= 78.5 cm2) A1
Note: Accept working in degrees.
[4 marks]