O-LevelMathematicsMensuration4024/21 · Oct/Nov 2018 · Q912 Marks
(a) [Volume of a sphere = 4/3 πr³] [Surface area of a sphere = 4πr²] The diagram shows lamp A. It is made in the shape of a cylinder with a hemisphere on top. The radius of the hemisphere and the radius of the cylinder are both 3 cm. The total height of the lamp is 24 cm. [Figure 9.1]
- (a)(i)Show that the volume of lamp A is 650 cm³, correct to 3 significant figures.[4]
- (a)(ii)Calculate the curved surface area of lamp A.[3]
- (a)(iii)Lamp B is mathematically similar to lamp A. The volume of lamp B is 450 cm³. Calculate the total height of lamp B.[2]
- (b)The mass of lamp C is 340 g, correct to the nearest 10 g. 8 of these lamps are placed in a packing case. The total mass of the packing case and the 8 lamps is 4.2 kg, correct to the nearest 0.1 kg. Calculate the upper bound of the mass of the packing case when empty. Give your answer in kilograms.[3]
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 2018). The mark or mark type is shown in brackets.
- [M3] = 650.3[...] or 650.4
- B1 for cylinder height = 21 soi
- M1 for π × 3^2 × their height
- M1 for 2/3 × π × 3^3
- A1
- [3] 452 or 452.3 to 452.4...
- M2 for 2 × π × 3^2 + π × 6 × 21
- or M1 for 2 × π × 3^2 or π × 6 × 21
- [2] 21.2 or 21.22 to 21.23...
- B1 for (450/650)^(1/3) soi or (650/450)^(1/3) soi
- [3] 1.57
- B1 for 4.25 or 335 used
- M1 for their 4.25 – 8 × their 335 ÷ 1000
- or for their 4250 - 8 × their 335
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