Question: how to find slant height with surface area?
Answer: Volume of a cone: V = (1/3)πr2h.
Slant height of a cone: s = √(r2 + h2)
Lateral surface area of a cone: L = πrs = πr√(r2 + h2)
Base surface area of a cone (a circle): B = πr. ... 
Total surface area of a cone: A = L + B = πrs + πr2 = πr(s + r) = πr(r + √(r2 + h2))