A severe thunderstorm dumped 2.9 in. of rain in 30 min on a town of area 32 km2. What volume of water, in acre-feet, fell on the town?
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To find the volume of water that fell on the town in acre-feet, we need to convert the given measurements and perform some calculations.
Here are the steps to solve the problem:
Step 1: Convert the area of the town from square kilometers to square feet.
- Recall that 1 square kilometer is equal to 1,000,000 square feet.
- Multiply the area of the town (32 km^2) by 1,000,000 to convert it to square feet.
- (32 km^2) * (1,000,000 ft^2/km^2) = 32,000,000 ft^2.
Step 2: Convert the rainfall from inches to feet.
- Recall that 1 foot is equal to 12 inches.
- Divide the given rainfall (2.9 inches) by 12 to convert it to feet.
- 2.9 in / 12 = 0.2417 ft (rounded to 4 decimal places).
Step 3: Calculate the volume of water using the formula: Volume = Area * Height.
- Multiply the area of the town (32,000,000 ft^2) by the rainfall in feet (0.2417 ft).
- 32,000,000 ft^2 * 0.2417 ft = 7,725,440 ft^3.
Step 4: Convert the volume from cubic feet to acre-feet.
- Recall that 1 acre-foot is equal to the volume of water required to cover one acre of land to a depth of one foot. It is approximately 43,560 cubic feet.
- Divide the volume of water in cubic feet (7,725,440 ft^3) by 43,560 to convert it to acre-feet.
- 7,725,440 ft^3 / 43,560 ft^2 = 177.36 acre-ft (rounded to 2 decimal places).
Therefore, the volume of water that fell on the town is approximately 177.36 acre-feet.