1. **State the problem:** We need to find the amount of paper required to make a paper wrap shaped like a cone with radius $r=3$ cm, height $h=7$ cm, and slant height $l=7.62$ cm. 2. **Formula used:** The paper wrap is a conical surface without the base, so the area required is the lateral surface area of the cone. The lateral surface area $A$ of a cone is given by: $$A = \pi r l$$ where $r$ is the radius and $l$ is the slant height. 3. **Calculate the lateral surface area:** Substitute $r=3$ cm and $l=7.62$ cm: $$A = \pi \times 3 \times 7.62 = 22.86\pi$$ 4. **Evaluate the numerical value:** Using $\pi \approx 3.1416$: $$A \approx 22.86 \times 3.1416 = 71.82 \text{ cm}^2$$ 5. **Conclusion:** The amount of paper required to make the wrap is approximately $71.82$ square centimeters.