Date | November 2021 | Marks available | 2 | Reference code | 21N.1.SL.TZ0.8 |
Level | Standard Level | Paper | Paper 1 | Time zone | Time zone 0 |
Command term | Find | Question number | 8 | Adapted from | N/A |
Question
Joey is making a party hat in the form of a cone. The hat is made from a sector, AOB, of a circular piece of paper with a radius of 18 cm and AÔB=θ as shown in the diagram.
To make the hat, sides [OA] and [OB] are joined together. The hat has a base radius of 6.5 cm.
Write down the perimeter of the base of the hat in terms of π.
Find the value of θ.
Find the surface area of the outside of the hat.
Markscheme
13π cm A1
Note: Answer must be in terms of π.
[1 mark]
METHOD 1
θ360×2π(18)=13π OR θ360×2π(18)=40.8407… (M1)
Note: Award (M1) for correct substitution into length of an arc formula.
(θ=) 130° A1
METHOD 2
θ360×π×182=π×6.5×18 (M1)
(θ=) 130° A1
[2 marks]
EITHER
130360×π(18)2 (M1)
Note: Award (M1) for correct substitution into area of a sector formula.
OR
π(6.5)(18) (M1)
Note: Award (M1) for correct substitution into curved area of a cone formula.
THEN
(Area=) 368 cm2 (367.566…, 117π) A1
Note: Allow FT from their part (a)(ii) even if their angle is not obtuse.
[2 marks]
Examiners report
Although most candidates understood what to do in part (a), many of them wrote a decimal approximation instead and did not give their answer in terms of π as required in this part. Many candidates were able to use the length of arc formula in (a)(ii). Some candidates went wrong with this question by confusing between the two values: 6.5 cm and 18 cm for the radius. In part (b), although candidates were able to find the surface area of the outside of the hat, several added the surface area of the base to their calculation. A few candidates used the cosine rule to find chord AB which was then used as the circumference of the base of the cone.
Although most candidates understood what to do in part (a), many of them wrote a decimal approximation instead and did not give their answer in terms of π as required in this part. Many candidates were able to use the length of arc formula in (a)(ii). Some candidates went wrong with this question by confusing between the two values: 6.5 cm and 18 cm for the radius. In part (b), although candidates were able to find the surface area of the outside of the hat, several added the surface area of the base to their calculation. A few candidates used the cosine rule to find chord AB which was then used as the circumference of the base of the cone.
Although most candidates understood what to do in part (a), many of them wrote a decimal approximation instead and did not give their answer in terms of π as required in this part. Many candidates were able to use the length of arc formula in (a)(ii). Some candidates went wrong with this question by confusing between the two values: 6.5 cm and 18 cm for the radius. In part (b), although candidates were able to find the surface area of the outside of the hat, several added the surface area of the base to their calculation. A few candidates used the cosine rule to find chord AB which was then used as the circumference of the base of the cone.