Let's calculate the required wire length and compare it with the roll's length. The room's perimeter consists of three straight segments and a quarter-circle. The straight segments are 4 m, 4 m, and 2 m. The quarter-circle has a radius of 2 m, so its length is 1/4 of the circumference of a full circle, calculated as 2 * π * R / 4 = π * R / 2. Substituting R = 2, we get π * 2 / 2 = π meters. Adding these together, the total wire length needed is 4 + 4 + 2 + π = 10 + 3.14 = 13.14 meters. If the roll contains 10 meters of wire, it will not be sufficient. Answer: No.