Lamps on a Lake

On a summer night, PX company decided to open their new branch of decorating lakes they distributed many lamps on Alhwiz lake. There are N lamps which are connected with batteries and each lamp has an electric power of 1 KW. These lamps are distributed uniformly across the lake's surface.

Sami has decided to take his girlfriend on a picnic using his Airship. He took her to this lake to show her how much he loves her and pretended that he has made this for her. Unfortunately, she doesn't believe him and she asks him about the number N of these lamps on the lake. He doesn't have much time to count them so he calls you and offer you 10K bucks if you can help him.

There is a sensor of light intensity on the airship measuring the light intensity coming from the lake to be 23.6 W. The lake's radius is 100 m and the airship's height is 100 m. Neglect the Interference and Diffraction effects. What is N? If you yielded non-integer value take the floor of it.

Assume that each point of the surface of the lake emits the same amount of energy as any other point.