O-LevelMathematicsMensuration4024/21 · May/June 2015 · Q812 Marks
The diagram shows a sector AOB of a circle with centre O and radius 9.3 cm. The angle of the sector is 260°.
- (a)(i)Calculate the length of the major arc AB.[2]
- (a)(ii)Calculate the area of the major sector AОВ.[2]
- (b)A sector of radius 0.8 cm, centre O, is removed from the sector AOB as shown in Diagram I. The shaded shape is used to make part of a conical funnel. AD is joined to BC as shown in Diagram II. The circumference of the top of the conical funnel is the major arc AB, and the circumference of the bottom of the conical funnel is the major arc CD.
- (b)(i)Calculate the external surface area of this part of the funnel.[2]
- (b)(ii)(a)The funnel is completed by attaching an open cylinder of height 5 cm to the bottom of the conical part. Show that the radius of the cylinder is 0.578 cm, correct to 3 significant figures.[2]
- (b)(ii)(b)Calculate the external curved surface area of this cylinder.[2]
- (b)(ii)(c)Calculate the volume of this cylinder.[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 2015). The mark or mark type is shown in brackets.
- [2] 42.18 to 42.22; M1 for (260/360) or 2π×9.3
- [2] 196 to 196.32; M1 for (260/360)×π×9.3²
- [2] 194 to 195; M1 for subtraction of two areas
- [2] 0.578 confirmed; M1 for (2πr =) (260/360)×2π×0.8
- [2] 18.1 to 18.2; M1 for 2π × 0.578 × 5
- [2] 5.24 to 5.25; M1 for π×0.578² × 5
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