General Mathematics Paper 2,Nov/Dec. 2010
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Question11

1.

5 cm

5 cm

6 cm

Q

N

R

P

The diagram is a right pyramid with a triangular base PQR and height |SN|. If |PQ| = 6 cm, |PR| = |RQ| = 5 cm, |PN| = 3.3 cm and ∠SPN = 52o, calculate, correct to two significant figures, the

1. vertical height |SN|;
2. area of base PRQ;
3. volume;
4. angle between the slant face SPQ and the base PRQ of the pyramid.

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Observation

This question was reported not to be popular among the candidates. The performance of those who attempted it was also said to be poor. Teachers were encouraged to emphasize the concept of three dimensional shapes by using appropriate instructional materials during teaching.
The height |SN| = |PN|tan52o = 4.2 cm. Height of the base PRQ =  =  = 4. Area of triangle PRQ =  x base x height =  x 6 x 4 = 12 cm2. Volume of pyramid =  x base area x height =  x 12 x 4.2      = 17 cm3, correct to 2 significant figures. If T is the midpoint of the line PQ, then the angle between the faces SPQ and PRQ = tan-1(STN) = tan-1( ) = 65o.