On June 17, heavy rain fell on Seattle for 26 min. at a rate of 3.9 mm/hr. if the area of Seattle is 144km^2, how many gallons of water fell on the city that day?
To determine the number of gallons of water that fell on Seattle that day, we'll need to follow these steps:
Step 1: Convert the area of Seattle from square kilometers (km^2) to square meters (m^2).
Step 2: Determine the volume of rainwater that fell on Seattle in cubic meters (m^3) by multiplying the rainfall rate (mm/hr) by the duration of the rainfall (min).
Step 3: Convert the volume of rainwater from cubic meters (m^3) to gallons (gal).
Let's compute each step:
Step 1: Convert the area of Seattle from square kilometers (km^2) to square meters (m^2).
1 km^2 = 1,000,000 m^2 (conversion factor)
Area of Seattle in square meters = 144 km^2 × 1,000,000 m^2/km^2
Area of Seattle in square meters = 144,000,000 m^2
Step 2: Determine the volume of rainwater that fell on Seattle in cubic meters (m^3).
1 mm/hr = 0.001 m/hr (conversion factor from mm to m)
Rainfall rate in meters per hour = 3.9 mm/hr × 0.001 m/mm
Rainfall rate in meters per hour = 0.0039 m/hr
Duration of rainfall in hours = 26 min ÷ 60 min/hr
Duration of rainfall in hours = 0.4333 hr
Volume of rainwater in cubic meters = Rainfall rate in meters per hour × Duration of rainfall in hours × Area of Seattle in square meters
Volume of rainwater in cubic meters = 0.0039 m/hr × 0.4333 hr × 144,000,000 m^2
Step 3: Convert the volume of rainwater from cubic meters (m^3) to gallons (gal).
1 cubic meter = 264.172 gallons (conversion factor)
Volume of rainwater in gallons = Volume of rainwater in cubic meters × 264.172 gal/cubic meter
Now, let's calculate the volume of rainwater in gallons:
Volume of rainwater in gallons = (0.0039 m/hr × 0.4333 hr × 144,000,000 m^2) × 264.172 gal/cubic meter
After calculating this expression, you'll have the number of gallons of water that fell on Seattle that day.
To find the number of gallons of water that fell on Seattle, we need to determine the total volume of rainwater first, and then convert it to gallons.
Step 1: Convert the area of Seattle from km² to m².
Given that 1 km² = 1,000,000 m², the area of Seattle in m² would be:
144 km² x 1,000,000 m²/km² = 144,000,000 m².
Step 2: Convert the rainfall rate from mm/hr to m/min.
Since there are 60 minutes in an hour, we can convert the rainfall rate as follows:
3.9 mm/hr ÷ 60 min/hr = 0.065 mm/min.
Step 3: Calculate the volume of rainwater in m³.
The volume of water is equal to the rainfall rate multiplied by the duration:
0.065 mm/min x 26 min = 1.69 mm of rain.
However, we need to convert millimeters (mm) to meters (m) for consistency:
1 mm = 0.001 m. Therefore, 1.69 mm = 1.69 x 0.001 = 0.00169 m.
Now, to calculate the volume, we multiply the area by the height:
Volume (m³) = Area (m²) x Height (m) = 144,000,000 m² x 0.00169 m = 243,360 m³.
Step 4: Convert the volume from cubic meters (m³) to gallons.
1 cubic meter (m³) is equivalent to 264.172 gallons, so we can convert the volume as follows:
243,360 m³ x 264.172 gallons/m³ = 64,244,787.52 gallons (approximately).
Therefore, approximately 64,244,787.52 gallons of water fell on Seattle that day.