Question 9
(A) A tailor had a piece of cloth in the shape of a trapezium. The perpendicular distance between the two parallel edges was 38 cm. The lengths of the two parallel edges are 46 cm and 60 cm. The tailor cut off a semi-circular piece of the cloth of radius 18 cm from the 60 cm edge. Calculate, correct to one decimal place, the area of the remaining piece of cloth. [Take ]
(B) Given that x litres of a chemical X, y litres of a chemical Y and z litres of chemical Z were mixed together to form a 1735 litres compound, with y= of x and z = of y, calculate,correct to the nearest litre, the value of x.
Observation
The Chief Examiner reported that this question was not popular with the candidates’. It was observed that only few candidates were able to the question satisfactorily.
In part (a), they were expected to first find the Area of trapezium by substituting into the formula to give = 2014cm2. The area of the semi-circle by substituting into the formula to give = 509.1427 cm2. The remaining area is area of trapezium – area of semi circle which gives 2014 – 509.1427 = 1504.85 = 1504.9 cm2.
Therefore, the remaining area = 1504.9 cm2.(1 d.p.)
In part (b), they were expected to form equation with the sentence to give
. Clearing fractions gives
Solving gives .