A-LevelMathematicsCircular measure9709/12 · Oct/Nov 2013 · Q26 Marks
Fig. 1 shows a hollow cone with no base, made of paper. The radius of the cone is 6 cm and the height is 8 cm. The paper is cut from A to O and opened out to form the sector shown in Fig. 2. The circular bottom edge of the cone in Fig. 1 becomes the arc of the sector in Fig. 2. The angle of the sector is θ radians. Calculate
- (i)the value of θ,[4]
- (ii)the area of paper needed to make the cone.[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 (Oct/Nov 2013). The mark or mark type is shown in brackets.
- [1] slant length = 10 cm.
- [1] circumference of base = 12π
- [1] arc length = 10θ ( = 12π) Use of rθ, θ calculated, not 6 or 8.
- [1] θ = 1.2π or 3.77 radians.
- [1] Use of ½r²θ with radians and r = calculated '10', not 6 or 8.
- [1] Area = 188.5 cm² or 60π.
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