O-LevelMathematicsMensuration4024/21 · Oct/Nov 2022 · Q118 Marks
[Figure 11.1] The diagram shows a regular pentagon ABCDE with centre O. AB = 6 cm and OA = d cm.
- (a)Show that d = 5.10 cm, correct to 2 decimal places.[3]
- (b)[Volume of a pyramid = 1/3 × base area × height] The regular pentagon ABCDE forms the base of a pyramid. The vertex F is vertically above O. The length of each sloping edge of the pyramid is 14 cm. Calculate the volume of the pyramid.[5]
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Mark scheme
Marking points from the official mark scheme (Oct/Nov 2022). The mark or mark type is shown in brackets.
- [3] (a) sin(their 72/2) = 3/d oe or cos(their 108/2) = 3/d oe; B1 for angle at centre = 72° or interior angle = 108° M1 their 72 angle at centre A1 their 108 interior angle 5.103 to 5.104
- [5] (b) 269 or 268.5 to 269.2; M2 for √(14²-5.10²) oe or M1 for 14² = h² +5.10² oe M2 for (1/3) × (5 × (1/2) × 5.10² × sin(their 72)) × their 13.04 oe or M1 for (1/2) × 5.10² × sin(their 72) oe or (1/2) × 3 × √(5.10²-3²)
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