At 100m from the antenna of a cellular base station in open country, measurements show that the power per square metre is 400µW/m2. What power per square metre could be expected at 200m from the base station? Show your working and explain any assumptions you make.
+37144 Area of circle at 100m = pi r^2 = pi (100^2) = 10,000 pi m^2
Total power = 10,000pi m^2 * 400 microwatts/m^2 = 4 x 10^6 pi microwatts
This total wattage will be distributed over a larger area at 200 m Area = pi (200^2) 40,000 pi m^2
Total watts/area = (4 x 10^6 pi microwatts) / (40,000 pi m^2) = 100 microwatts/m^2
I am not sure where you are in your studies, so I will edit this question assuming you are working on surface areas of SPHERES (Answer is the same)
Surface area of a SPHERE = 4 pi r^2 = 4 pi (100^2) = 40,000 pi m^2
40,000 pi m^2 * 400 microwattats/m^2 = 16 x 10^6 pi microwatts
at 200 m area = 4 pi (200^2) = 160,000 pi m^2
( 16 x10^6 pi microwatts) / (160000 pi m^2) = 1 x 10^2 microwatts/m^2
