O-LevelMathematicsMensuration4024/22 · May/June 2014 · Q912 Marks

[Volume of a cone = (1/3)πr²h] [Curved surface area of a cone = πrl] The diagram shows a solid cone of height 15 cm and base radius 6 cm. [Figure of a cone with height 15 and radius 6 indicated]

(a)Show that the slant height of the cone is 16.2cm, correct to one decimal place.[1]
(b)Calculate the total surface area of the cone.[3]
(c)Calculate the volume of the cone.[2]
(d)The cone is made from wood. The mass of 1m³ of the wood is 560kg. Calculate the mass of the cone in grams.[2]
(e)(i)Another cone is made of the same material and is geometrically similar to the first. The mass of the second cone is double the mass of the first. Calculate the height of the second cone.[2]
(e)(ii)Calculate the total surface area of the second cone.[2]

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Mark scheme

Marking points from the official mark scheme (May/June 2014). The mark or mark type is shown in brackets.

[1] (a) √15² +6² = 16.15(5...)
[1] (a) Must be shown to at least 2 d.p.
[3] (b) 417 to 419
[3] (b) M1 for π × 6 × 16.2 soi by 305.4 M1 for π × 6² soi by 113.1
[2] (c) 565 to 566
[2] (c) M1 for 1/3 × π × 6² × 15 or better
[2FT] (d) 316 to 317
[2FT] (d) FT their (c) × 0.56 evaluated B1 for figs 316(...) or 317(...) or their (c) × figs 56 evaluated
[2] (e)(i) 18.89 to 18.9
[2] (e)(i) M1 for ³√2 or 1.25... seen oe
[2] (e)(ii) 662 to 665
[2] (e)(ii) M1 for (³√2)² or 1.58... seen oe

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