A party hat is a cone without a base. It has radius 7 cm and height 24 cm…

Step 1. The slant height. $l = \sqrt{7^2 + 24^2}\ \text{cm} = \sqrt{625}\ \text{cm} = 25\ \text{cm}$.

Step 2. The area. $\pi r l = \dfrac{22}{7} \times 7\ \text{cm} \times 25\ \text{cm} = 550\ \text{cm}^2$. In exact form it is $175\pi\ \text{cm}^2$, about $549.8\ \text{cm}^2$.

Step 3. The sector. The angle is $\dfrac{r}{l} \times 360^\circ = \dfrac{7}{25} \times 360^\circ = 100.8^\circ$.