O-LevelMathematicsMensuration4024/22 · Oct/Nov 2018 · Q911 Marks
[Volume of a pyramid = (1/3) × base area × height] [Figure 9.1] The diagram shows a pyramid with a rectangular, horizontal base. Vertex F of the pyramid is vertically above the centre of the base, E. AB = 6.2 cm and BC = 4.3 cm. The length of each sloping edge of the pyramid is 9.5 cm. (a) Show that the height, EF, of the pyramid is 8.72 cm, correct to 3 significant figures.
- (a)Show that the height, EF, of the pyramid is 8.72 cm, correct to 3 significant figures.[4]
- (b)Calculate the volume of the pyramid.[2]
- (c)Calculate angle AFB.[3]
- (d)Calculate the angle of elevation of F from the midpoint of AB.[2]
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Mark scheme
Marking points from the official mark scheme (Oct/Nov 2018). The mark or mark type is shown in brackets.
- [4] M2 for AC² = 4.3² + 6.2² oe
- [4] or FX² + (4.3/2)² = 9.5² or FY² + (6.2/2)² = 9.5²
- [4] M1 for EF² = 9.5² – their AE² oe
- [4] or EF² = theirFX² – (6.2/2)²
- [4] or EF² = theirFY² – (4.3/2)²
- [4] A1
- [2] M1 for 1/3 × 6.2 × 4.3 × 8.72
- [3] M2 for 2sin^-1 (3.1/9.5) oe
- [3] or M1 for sin^-1 (3.1/9.5) oe
- [3] Alternative method:
- [3] M2 for cos AFB = (9.5² + 9.5² – 6.2²) / (2 × 9.5 × 9.5)
- [3] or M1 for 6.2² = 9.5² + 9.5² – 2 × 9.5 × 9.5 × cos AFB
- [2] M1 for tan[...] = 8.72 / (4.3/2) oe
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