O-LevelMathematicsMensuration4024/22 · Oct/Nov 2019 · Q89 Marks
[Volume of cone = (1/3)πr²h] [Curved surface area of a cone = πrl] The diagram shows a bowl with a circular base. The curved surface of the bowl is formed by removing a cone with radius 12cm and height 45 cm from a larger cone as shown in the diagram. The radius of the top of the bowl is 16 cm and its height is 15 cm.
- (a)Calculate the volume of the bowl.[3]
- (b)The slant height of the cone that has been removed is c cm. Show that c = 46.6, correct to 3 significant figures.[2]
- (c)The bowl is completely filled with water. Calculate the total surface area of the bowl that is in contact with the water.[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 2019). The mark or mark type is shown in brackets.
- [3] 9300 or 9299 to 9301
- [3] M2 for (1/3)π×16^2×60 - (1/3)π×12^2×45 oe
- [3] or M1 for (1/3)π×16^2×60 or (1/3)π×12^2×45
- [2] [c^2=]12^2+45^2
- [2] M1
- [2] [c=]46.57...
- [2] A1
- [4] 1820 or 1816 to 1819.[0...]
- [4] B2 for l = 62.09 to 62.13
- [4] or M1 for √60^2 +16^2 oe
- [4] and M1 for π×16×their 62.1 – π×12×46.6 [+π×12^2]
- [4] If 0 scored, SC1 for π×12^2
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