1. The problem asks to identify the mistake Beth made when calculating the curved surface area of the cone. 2. The formula for the curved surface area of a cone is $$\text{Curved surface area} = \pi r l$$ where $r$ is the radius and $l$ is the slant height. 3. From the diagram, the radius $r = 5$ cm and the slant height $l = 13$ cm. 4. Beth calculated the curved surface area as $$\pi \times 5 \times 12 = 60\pi$$ cm², but she used the vertical height (12 cm) instead of the slant height (13 cm). 5. The correct calculation should be $$\pi \times 5 \times 13 = 65\pi$$ cm². 6. Therefore, the mistake Beth made was using the vertical height instead of the slant height in the formula for curved surface area. Final answer: Beth should have used the slant height 13 cm, not the vertical height 12 cm, in the formula.