A severe thunderstorm dumped 2.4 in of rain in 30 min on a town of area 35 km^2. What mass of water (in kg) fell on the town? One cubic meter of water has a mass of 103 kg.
To find the mass of water that fell on the town, we need to calculate the volume of water using the given information, and then convert it to mass using the density of water.
First, let's convert the area from square kilometers (km^2) to square meters (m^2). Since 1 km^2 = 1,000,000 m^2, we can multiply the area by 1,000,000 to get the area in square meters.
Area of the town = 35 km^2 = 35 × 1,000,000 m^2 = 35,000,000 m^2
Now, we need to convert the amount of rain from inches (in) to meters (m). Since 1 inch = 0.0254 meters (approximately), we can multiply the amount of rain by 0.0254 to get the amount in meters.
Amount of rain = 2.4 in × 0.0254 m/in = 0.06096 m
Next, we need to calculate the volume of water using the area and the amount of rain. Since volume = area × height, the volume of water that fell on the town is:
Volume of water = Area × Amount of rain = 35,000,000 m^2 × 0.06096 m = 2,136,600 m^3
Finally, to convert the volume of water into mass, we can use the density of water. Given that 1 cubic meter of water has a mass of 103 kg, we can multiply the volume by the density to get the mass.
Mass of water = Volume of water × Density of water = 2,136,600 m^3 × 103 kg/m^3 = 220,033,800 kg
Therefore, a mass of approximately 220,033,800 kg of water fell on the town during the severe thunderstorm.