The basic formula for the lateral surface area of a cone is


    A = ,      (1)


where A is the lateral surface area, H is the slant height and "s" is the circumference of the base of the cone.


When students study the lateral surface area of a cone, they start from this formula, so I will assume that you are familiar with it.



    If not, then you can derive it mentally and momentarily in your mind, presenting the lateral surface area 

    of  cone as the union of surface area of many narrow triangles with the common peak vertex at the cone's vertex.



The last step in my explanation is the formula  


    s =       (2)


for the base circumference.  Here  "r"  is the cone's radius (= the radius of the base).


As soon as you substitute  (2)  into (1), you will obtain what you need.