Calculating Storm Rainfall Using Polar Coordinates

You volunteer at a local emergency preparedness center during storm season. A storm system is approaching your area, and the weather radar displays precipitation intensity as a function of distance and angle from the radar station located at the center of town. The radar measures rainfall rate in centimeters per hour at each point in the region. Your task is to analyze the radar data to calculate total rainfall amounts over different neighborhoods. This information helps emergency coordinators decide where to position response teams and sandbag supplies. The radar naturally provides data in polar coordinates, with distance [latex]r[/latex] measured in kilometers from the station and angle [latex]\theta[/latex] measured from due east.