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 AOB = 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.

$13 \pi$ cm (A1) Note: Answer must be in terms of $\pi$.

METHOD 1 $\frac{\theta}{360} \times 2 \pi(18)=13 \pi$ OR $\frac{\theta}{360} \times 2 \pi(18)=40.8407 ...$ (M1) Note: Award (M1) for correct substitution into length of an arc formula. $(\theta=) 130^{\circ}$ (A1)

METHOD 2 $\frac{\theta}{360} \times \pi \times 18^{2}=\pi \times 6.5 \times 18$ $(\theta=) 130$ (A1)

EITHER $\frac{130}{360} \times \pi(18)^{2}$ Note: Award (M1) for correct substitution into area of a sector formula. OR $\pi(6.5)(18)$ Note: Award (M1) for correct substitution into curved area of a cone formula.

THEN (Area $=$ ) 368 cm$^2$ (367.566..., $117\pi$) (A1) Note: Allow $FT$ from their part (a)(ii) even if their angle is not obtuse.