General Mathematics Paper 2,Nov/Dec. 2010
 Questions: 1 2 3 4 5 6 7 8 9 10 11 12 13 Main
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Question 3

1. A cube of side 4 cm has the same volume as a cone with diameter 7 cm. Calculate, correct to the nearest cm, the height of the cone.  [Take π = ].

36 cm

Y

X

O

In the diagram, O is the centre of the circle, radius 14 cm. If the length of the minor arc                  XY is 36 cm, calculate the area of the minor sector OXY. [Take π = ].

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Observation

It was reported that while this question was also popular among the candidates, their performance was poorer than it was in Questions 1 and 2.  It was reported that poor understanding as well as poor application of the formulae was observed among some candidates.
In part (a), candidates did not equate the volume of the cone to that of a cube correctly as expected. Some others wrongly used the value for the diameter as of the radius of the cone. It was also reported that some candidates did not write their final answer to the required degree of accuracy. Candidates were expected to obtain the volume of the cube and equate it to that of a cone as l3 = r2h. i.e. 43 =  h, where h is the height of the cone. Therefore,         h =  = 5 cm to the nearest centimeter.
In part (b), candidates were expected to find the angle, (say, x), subtended by the arc at the centre of the circle and use it to calculate the required area i.e. 36 = . Therefore, x =  =
Area =  x  x 142 =  = 252 cm2.