O-LevelMathematicsMensuration4024/22 · May/June 2018 · Q59 Marks
OAB is a sector of a circle, centre O, radius 11 cm. AOB = 134°. [Figure: sector OAB with radius 11cm and angle 134 degrees] A cone has height 9.5 cm and volume 115cm³. [Figure: cone with height 9.5 and dashed radius]
- (a)(i)Calculate the length of the arc AB.[2]
- (a)(ii)Calculate the shortest distance from O to the line AB.[2]
- (b)(i)Show that the radius of the base of the cone is 3.4cm, correct to 1 decimal place.[2]
- (b)(ii)Calculate the curved surface area of the cone.[3]
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.
- [2] M1 for 134/360 × 2 × π × 11 oe
- [2] M1 for 11 cos (134/2) or 11 sin ((180-134)/2) oe
- [2] M1 Correct substitution into volume equation or correct rearrangement
- A1
- [3] M2 for π×3.4×√9.5^2 +3.4^2 or M1 for l^2 = 9.5^2 +3.4^2 soi
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