Note: I think there is a mistake in the question that you have written down. The diameter of the wire should be 1 m and not 1 cm, as that would otherwise give us very long length of the wire. The units of the diameter of wire and the diameter of the cone should be same (either cm or m). Here, we have considered it to be m.
Let triangle ABC represent the 2D representation of cone such that angle(BAC) = 60. Draw a perpendicular AM from A to the side BC. AM represents the height of the cone and hence, is equal to 20m.
Also, the cone is cut into 2 parts at the middle of the height, so draw a line parallel to BC and passing through a point N on AM such that AN = NM = 10 m and the line intersects side AB and AC at points D and E respectively.