O-LevelMathematicsMensuration4024/21 · Oct/Nov 2017 · Q812 Marks

[Volume of a cone = 1/3 πr²h] [Curved surface area of a cone = πrl] [Volume of a sphere = 4/3 πr³] [Surface area of a sphere = 4πr²] The diagram shows solid A which is made from a hemisphere joined to a cone of equal radius. The hemisphere and the cone each have radius 6cm. The total height of the solid is 18 cm.

(a)Show that the slant height, xcm, of the cone is 13.4 cm, correct to 1 decimal place.[2]
(b)Calculate the total surface area of solid A.[3]
(c)Calculate the volume of solid A.[3]
(d)(i)Calculate the surface area of solid B correct to 3 significant figures.[2]
(d)(ii)Calculate the volume of solid C correct to 3 significant figures.[2]

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] M1 for [x² =] 6² + 12² or [x =]√62 +122
[2] A1 [x = ] 13.41[6...] or 13.42
[3] M1 for 1/2 × 4π × 6² seen
[3] M1 for π × 6 × 13.4 seen
[3] After 0 scored, SC1 for consistent use of r = 3 in formula for [hemi]sphere and cone
[3] 478.7 to 479.4
[3] M1 for 1/3 × π × 6² × 12 seen
[3] M1 for 1/2 × 4/3 × π × 6³ seen
[3] After 0 scored, SC1 for consistent use of r = 3 in formula for [hemi]sphere and cone
[3] 904.7 to 905 nfww
[2] M1 for (6/2)² soi
[2] 4310 or FT 9 × their (b)
[2] M1 for (1/2)³ soi
[2] 113 or FT 1/8 × their (c)

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