O-LevelMathematicsMensuration4024/21 · May/June 2016 · Q712 Marks
(a) [Figure 7.1] AC is a diameter of the circle, centre O, radius 5 cm. ACB = 64°. Calculate the length of the minor arc BC. (b) [Figure 7.2] A baking tray is an open cylinder of radius 15.5 cm with a rim. The outer edge of the rim is a circle of radius 16.5 cm.
- (a)AC is a diameter of the circle, centre O, radius 5 cm. ACB = 64°. Calculate the length of the minor arc BC.[4]
- (b)(i)Calculate the area of the top surface of the rim.[2]
- (b)(ii)44 identical circular holes are cut out of the bottom of the baking tray. The area of the bottom that remains is 650 cm². Calculate the radius of each circular hole.[3]
- (b)(iii)[Figure 7.3] To make a pizza, the baking tray is completely filled with dough to a depth of d mm. The open cylinder holds 500 cm³ of dough. Calculate the depth of the dough, d mm, giving your answer correct to the nearest millimetre.[3]
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Mark scheme
Marking points from the official mark scheme (May/June 2016). The mark or mark type is shown in brackets.
- [4] (a) 4.53 to 4.54
- [4] (a) B2 for BOC = 52 or after BO
- [4] (a) B1 for ABC = 90 or triangle OBC isosceles or BAC = 26
- [4] (a) M1 for (52/360) × 2π5 ft
- [2] (b)(i) 101 or 32π or 100 to 100.6
- [2] (b)(i) M1 for π(16.5^2) or 15.5^2
- [3] (b)(ii) 0.87 to 0.871
- [3] (b)(ii) B1 for π15.5^2 or 44πr^2 and π15.5^2 - 650
- [3] (b)(ii) M1 for r^2 = ((π15.5^2 – 650) / (44π))
- [3] (b)(iii) 7
- [3] (b)(iii) M1 for π15.5^2d = 500
- [3] (b)(iii) A1 for 0.66 to 0.663
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