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?

convert km^2 to in^2

convert gal to in^3

divide the area (in^2) by the volume (in^3) to find the rain depth

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To find the number of inches of rain that fell during the 18-minute period, we need to convert gallons to inches.

Step 1: Convert the area from km² to square inches.
1 km² = 10^6 m² = (10^6 m * 100 cm/m * 1 inch/2.54 cm)^2 = (10^6 * 100/2.54)^2 in² = 1.55 * 10^10 in²

Step 2: Convert the volume in gallons to cubic inches.
1 gal = 231 in³

Volume = 1.42 * 10^9 gal * 231 in³/gal = 3.28 * 10^11 in³

Step 3: Divide the volume of rain by the area to find the depth of rain in inches.
Depth = Volume/Area = (3.28 * 10^11 in³) / (1.55 * 10^10 in²)
Depth = 21.16 inches

Therefore, during the 18-minute period, approximately 21.16 inches of rain fell.

To find the number of inches of rain that fell during the 18-minute period, we need to convert the given amount of rain from gallons to inches.

Step 1: Convert km^2 to square inches
1 km^2 = 1,000,000 m^2 (Since there are 1000 meters in a kilometer)
1 m^2 = 1550.0031 in^2 (Since there are approximately 1550.0031 square inches in a square meter)

So, 76.0 km^2 = 76,000,000 m^2
76,000,000 m^2 = 76,000,000 * 1550.0031 in^2 ≈ 118,110,236,000 in^2

Step 2: Convert gallons to cubic inches
1 gallon = 231 in^3 (Since there are 231 cubic inches in a gallon)

So, 1.42 * 10^9 gal ≈ 1.42 * 10^9 * 231 in^3 ≈ 328.02 * 10^9 in^3

Step 3: Convert cubic inches to inches
To convert cubic inches to inches, we need to divide the previous result by the area in square inches.

So, 328.02 * 10^9 in^3 ÷ 118,110,236,000 in^2 = 2.78 inches

Therefore, during the 18-minute period, approximately 2.78 inches of rain fell.