To find the slant height, we can use the Pythagorean Theorem.
According to the information given, the height of the cone (h) is 6 cm and the diameter of the base (d) is 13 cm.
Using the Pythagorean Theorem:
h^2 + (d/2)^2 = l^2
6^2 + (13/2)^2 = l^2
36 + 42.25 = l^2
78.25 = l^2
l ≈ √78.25
l ≈ 8.8 cm
Therefore, the slant height should be approximately 8.8 cm.
So the answer is 8.8 cm.