O-LevelMathematicsMensuration4024/22 · Oct/Nov 2015 · Q812 Marks
OAB is a sector of a circle, centre O, radius 6 cm. AOB = 25°. Calculate the length of the arc AB.
- (a)(i)OAB is a sector of a circle, centre O, radius 6 cm. AOB = 25°. Calculate the length of the arc AB.[2]
- (a)(ii)Calculate the area of the sector OAB.[2]
- (b)(i)The sector OAB from part (a) is the cross-section of a slice of cheese. The slice has a height of 5 cm. Calculate the volume of this slice of cheese.[1]
- (b)(ii)Calculate the total surface area of this slice of cheese.[3]
- (b)(iii)Another 25° slice of cheese has 3 times the height and twice the radius. Calculate its volume.[2]
- (c)(i)A dairy produces cylindrical cheeses, each with a volume of 800 cm³. The height h cm and the radius r cm can vary. Express h in terms of r.[1]
- (c)(ii)What happens to the height if the radius is doubled?[1]
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Mark scheme
Marking points from the official mark scheme (Oct/Nov 2015). The mark or mark type is shown in brackets.
- [2] M1 for 25/360 × 2π × 6
- 2.62
- [2] M1 for 25/360 × π × 6²
- 7.85
- [1ft] 39.3
- [3ft] B1 for 30 or 60 or M1 for 5× (a)(i) and indep M1 for 2×(a)(ii)
- 88.8
- [2ft] B1 for height = 15 and radius = 12 soi
- 471 to 472
- [1] (h =) 800/πr²
- [1] h is divided by 4 oe
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