Step 1 :Given that the diameter of the cone is 10 inches, we can find the radius r which is half of the diameter. So, \(r = \frac{10}{2} = 5\) inches.
Step 2 :The slant height l is given as 8 inches.
Step 3 :The surface area A of a cone is given by the formula \(A = \pi r(r + l)\).
Step 4 :Substitute the values of r and l into the formula: \(A = \pi * 5 * (5 + 8)\).
Step 5 :Simplify the expression to find the surface area: \(A = \pi * 5 * 13 = 65\pi\) square inches.
Step 6 :\(\boxed{A = 65\pi}\) square inches is the surface area of the cone.