O-LevelMathematicsMensuration4024/21 · May/June 2018 · Q99 Marks
The diagram shows a sector of a circle of radius 8 cm and angle 70°.
- (a)Calculate the shaded area.[4]
- (b)A piece of chocolate is in the shape of a prism with the shaded area from part (a) being its cross section. The rectangular base of the chocolate is 16cm by x cm. The piece of chocolate is to be placed in a box which is a cuboid of size 16cm by x cm by 1.5 cm.
- (b)(i)Show that the chocolate will fit inside the box.[3]
- (b)(ii)These boxes are to be packed in cartons in the shape of a cuboid. The size of each carton is 48 cm by 4x cm by 24 cm. Find the maximum number of boxes that can be packed inside one carton.[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 (May/June 2018). The mark or mark type is shown in brackets.
- [4] 9.025 to 9.03
- [4] M3 for (70/360) * π * 8² - (1/2) * 8² * sin 70
- [4] or M1 for (70/360) * π * 8²
- [4] or M1 for (1/2) * 8² * sin 70
- [3] 8 - 8cos 35 oe
- [3] 1.45 or 1.446 to 1.447 so yes
- [3] M2 M1 for 8cos 35 (= 6.55..)
- [3] A1
- [2] 192
- [2] B1 for two of 4, 16 and 3 soi
- [2] or M1 for (48 * 4x * 24) / (16 * x * 1.5) oe
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