O-LevelMathematicsMensuration4024/22 · Oct/Nov 2017 · Q912 Marks
(a) The ventilation shaft for a tunnel is in the shape of a cylinder. The cylinder has radius 0.4m and length 15 m. (b) The diagram shows the cross-section of the tunnel. [Figure of a segment of a circle] The cross-section of the tunnel is a major segment of a circle, centre O. The radius of the circle is 4.5m and AÔB = 110°. (c) The length of the tunnel is 1750m. A car drives through the tunnel at an average speed of 45 km/h. Work out the time the car takes to travel through the tunnel. Give your answer in minutes and seconds. (d) The diagram shows the position of the tunnel entrance, T, and two road junctions, P and Q, on horizontal ground. [Figure with P, Q, T and bearings] Q is due north of P and T is on a bearing of 062° from P. PT = 450 m and QT = 720m.
- (a)Calculate the volume of the cylinder.[2]
- (b)Calculate the area of the cross-section of the tunnel.[4]
- (c)Work out the time the car takes to travel through the tunnel. Give your answer in minutes and seconds.[2]
- (d)Calculate the bearing of T from Q.[4]
This question uses a diagram from the original paper, which isn't shown here. Open the full paper from the past papers archive to see it.
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2017). The mark or mark type is shown in brackets.
- [2] (a) 7.54
- M1 for π × 0.42 × 15
- [4] (b) 53.7
- M1 for 1/2 × 4.52 x sin 110 ое
- M1 for 250/360 × π × 4.52 or 110/360 × π × 4.52
- M1 for their 9.514 + their 44.18 oe
- [2] (c) 2 minutes 20 seconds
- M1 for figs 175 ÷ 45 soi
- [4] (d) 146.5°
- B3 for 33.5°
- Or M2 for sin Q = (450 sin 62) / 720
- Or M1 for sin Q / 450 = sin 62 / 720
- AND M1 for 180 - their Q
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