Question 11
The diagram shows the cross section of a bridge with a semi circular hollow in the middle. If the perimeter of the cross section is 34 m, calculate the:
(i) length PQ;
(ii) area of the cross section.
Observation
The Chief Examiner reported that this question was quite popular among the candidates as majority of them attempted it. However, while their performance in part (a) was reported good, that of part (b) was poor. Majority of them were reported not to obtain the length │PQ│.
In part (a), majority of them were reported to obtain the required ratio p:q = 4:1. However, a few of them got it wrong by interchanging the ratio i.e. p:q = 1:4. Candidates were expected to cross-multiply both sides of the equality sign to obtain 3p + 4q = 6p – 8q. Bringing like terms together gave 12q = 3p. Dividing both sides by 3q gave 4/1 = p/q which implied that p:q = 4:1.
