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To find the slant height of the cone, we can use the Pythagorean Theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
Given:
Height (h) = 6 cm
Diameter (d) = 13 cm
Radius (r) = d/2 = 13/2 = 6.5 cm
Let the slant height be represented as L.
We can set up the right triangle with the height, radius, and slant height as the sides:
h^2 + r^2 = L^2
(6)^2 + (6.5)^2 = L^2
36 + 42.25 = L^2
78.25 = L^2
L = √78.25
L ≈ 8.8 cm
Therefore, the slant height of the cone should be approximately 8.8 cm.