A severe thunderstorm dumped 2.4 in of rain in 30 min on a town of area 35 km2. What mass of water (in kg) fell on the town? One cubic meter of water has a mass of 103 kg.
Time is extraneous in this problem.
Mass = Volume x Density
Volume = [35 x 1000 x 1000 m^2] [2.4 x 2.54 / 100 m] = 2,133,600 m^3
Density = 103 kg / m^3
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Mass of rain that fell = 2,133,600 m^3 x 103 kg / m^3 = 219,760,800 kg
To find the mass of water that fell on the town, we need to find the volume of water first, and then convert it to mass.
1. Find the volume of water:
- Convert the area of the town from km² to m²:
35 km² = 35,000,000 m² (1 km² = 1,000,000 m²)
- Convert the rainfall from inches to meters:
1 inch = 0.0254 meters
2.4 inches = 2.4 x 0.0254 meters = 0.06096 meters
- Multiply the area by the height (rainfall) to find the volume:
Volume = Area x Height
Volume = 35,000,000 m² x 0.06096 meters = 2,139,600 cubic meters
2. Convert the volume to mass:
One cubic meter of water has a mass of 103 kg.
Mass = Volume x Mass per Volume
Mass = 2,139,600 cubic meters x 103 kg/m³ = 220,399,800 kg
Therefore, the mass of water that fell on the town is 220,399,800 kg.
To find the mass of water that fell on the town, we need to calculate the volume of the rainwater and then convert it to mass using the given density.
First, let's convert the area of the town to square meters:
1 km^2 is equal to 1,000,000 square meters.
Therefore, the area of the town in square meters is 35 km^2 * 1,000,000 square meters/km^2 = 35,000,000 square meters.
Next, we need to find the volume of the rainwater. To do that, we'll multiply the area by the height (rainfall):
Volume = area * height.
The rainfall is given as 2.4 inches of rain, which we need to convert to meters. 1 inch is equal to 0.0254 meters.
Therefore, the rainfall in meters is 2.4 inches * 0.0254 meters/inch = 0.06096 meters.
Now, we can calculate the volume:
Volume = 35,000,000 square meters * 0.06096 meters = 2,134,600 cubic meters.
Since we know the density of water is 103 kg/m^3, we can multiply the volume by the density to find the mass:
Mass = 2,134,600 cubic meters * 103 kg/m^3 = 219,903,800 kg.
Therefore, the mass of water that fell on the town is 219,903,800 kg.