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Height = 4,800 × 0.5 = <<4800*0.5=2400>>2,400 meters.
Area = 1,600 × 2,400 = <<1600*2400=3840000>>3,840,000 square meters.
Convert to square kilometers: 3,840,000 ÷ 1,000,000 = <<3840000/1000000=3.84>>3.84 km².
A cartographer is calculating the gradient of a mountain trail that rises from 850 meters to 2,150 meters over a horizontal distance of 12.5 kilometers. What is the percent grade of the trail?
Elevation gain = 2,150 − 850 = <<2150-850=1300>>1,300 meters.
Horizontal distance = 12.5 km = 12,500 meters.
Percent grade = (rise ÷ run) × 100 = (1,300 ÷ 12,500) × 100 = <<1300/12500*100=10.4>>10.4%.
A cartographer is projecting a cylindrical map of longitude and latitude using the Mercator projection. If the true width of a region between 0° and 6° east longitude is 420 kilometers, and the map scale at the equator is 1:10,000,000, what is the width of this region on the map in centimeters?
Actual distance = 420 km = 420,000 meters.
Scale: 1 cm = 10,000 meters, so map width = 420,000 ÷ 10,000 = <<420000/10000=42>>42 cm.
