O-LevelMathematicsMensuration4024/21 · Oct/Nov 2016 · Q610 Marks
The four walls of a building are faces of a cuboid ABCDEFGH. T is vertically above C and G, so ABT = ADT = 90°. The cuboid has length 9m, width 8 m and height 5 m. TC = 6m. [Figure 6.1]
- (a)Calculate the length of DT.[2]
- (b)The roof is formed by four triangles, ABT, BCT, CDT and DAT. Calculate the total surface area of the roof.[3]
- (c)[The volume of a pyramid is (1/3) × area of base × perpendicular height] Calculate the total volume of the building.[2]
- (d)Calculate the angle of elevation of T from H.[3]
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Mark scheme
Marking points from the official mark scheme (Oct/Nov 2016). The mark or mark type is shown in brackets.
- [2] (a) [DT= ]10.8 or 10.816 to 10.82 M1 for DT² = 6² + 9² oe
- [3] (b) 139 or 139.2 to 139.3 B1 for BT = 10 M1 for sum of areas of four triangles seen, with at least 3 of the following correct: (1/2)×8×6, (1/2)×9×6, (1/2)×8×their DT, (1/2)×9×their BT
- [2] (c) 504 M1 for 9 × 8 × 5 or (1/3)×9×8×6
- [3] (d) 50.7° final answer M1 for finding an acute angle in triangle THG. e.g. tan [...] = 11/9 or tan [...] = 9/11 A1 for 50.7[...]° or 39.28 to 39.3°
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