During a typical afternoon thunderstorm in the summer, an area of 76.0 km2 receives 1.42 * 10^9 gal of rain in 18 min. How many inches of rain fell during this 18 min period?
To calculate how many inches of rain fell during the 18-minute period, we need to convert the given volume of rain from gallons to inches. Here are the steps to get the answer:
Step 1: Convert the area from square kilometers to square inches.
To convert from square kilometers to square inches, we need to know the conversion factor between the two units. 1 square kilometer is equal to 1,550,003,100 square inches. Therefore, to convert 76.0 km^2 to square inches, we multiply it by the conversion factor:
Area in square inches = 76.0 km^2 * 1,550,003,100 square inches/km^2
Step 2: Convert the volume of rain from gallons to cubic inches.
To convert from gallons to cubic inches, we need to know the conversion factor between the two units. 1 gallon is equal to 231 cubic inches. Therefore, to convert 1.42 * 10^9 gallons to cubic inches, we multiply it by the conversion factor:
Volume in cubic inches = 1.42 * 10^9 gallons * 231 cubic inches/gallon
Step 3: Calculate the depth of rain in inches.
The depth of rain in inches is equal to the volume of rain in cubic inches divided by the area in square inches:
Depth of rain in inches = Volume in cubic inches / Area in square inches
Now, let's calculate the answer:
Area in square inches = 76.0 km^2 * 1,550,003,100 square inches/km^2 = 117,400,236,400 square inches
Volume in cubic inches = 1.42 * 10^9 gallons * 231 cubic inches/gallon = 328,020,000,000 cubic inches
Depth of rain in inches = 328,020,000,000 cubic inches / 117,400,236,400 square inches = 2.794 inches
Therefore, approximately 2.794 inches of rain fell during the 18-minute period.