A heavy rainstorm dumps 1.0 cm of rain on a city 8 km wide and 9 km long in a 2 hour period.

How many metric tons (1 metric ton = 10^3 kg) of water fell on the city? (1 cm^3 of water has a mass of 1g = 10^-3 kg)

What I have thus far:

72 km^2 x (1E^10 cm^2/1km^2) x (10^-3 kg/ cm^3) x (1 metric ton/ 10^3 kg)

you forgot the depth: 1cm

Though it makes the units come out, it does not affect the final numerical value.

Looks good.

To find the number of metric tons of water that fell on the city, you need to calculate the volume of the rainwater and then convert it to metric tons.

First, let's calculate the volume of the rain by multiplying the area of the city (width x length) by the depth of the rain.

Area of the city = 8 km x 9 km = 72 km^2.

Since the depth of the rain is given as 1.0 cm, we need to convert it to meters. (1 cm = 0.01 m)

Depth of the rain = 0.01 m.

Now, calculate the volume of the rain:

Volume = Area x Depth = 72 km^2 x 0.01 m = 0.72 km^3.

To convert the volume to cubic meters, we need to multiply by 1E+9 (since 1 km^3 = 1E+9 m^3).

Volume = 0.72 km^3 x 1E+9 m^3/km^3 = 0.72E+9 m^3.

Next, let's convert the volume of rainwater to kilograms:

1 m^3 of water has a mass of 1,000 kg.

Mass = Volume x Density = 0.72E+9 m^3 x 1,000 kg/m^3 = 0.72E+12 kg.

Finally, let's convert the mass to metric tons:

1 metric ton = 1,000 kg.

Metric tons = Mass / 1,000 = 0.72E+12 kg / 1,000 = 0.72E+9 metric tons.

So, approximately 0.72 billion metric tons of water fell on the city during the rainstorm.

To calculate the number of metric tons of water that fell on the city, we need to multiply the area of the city by the depth of the rain and convert the units appropriately. Here are the step-by-step calculations:

1. Convert the dimensions of the city from kilometers to centimeters:
- Width: 8 km = 8,000 m = 800,000 cm
- Length: 9 km = 9,000 m = 900,000 cm

2. Calculate the area of the city in square centimeters:
- Area = Width x Length = 800,000 cm x 900,000 cm = 720,000,000,000 cm^2

3. Convert the depth of the rain from centimeters to cubic centimeters:
- Depth = 1.0 cm = 1.0 cm^3

4. Calculate the volume of water that fell on the city in cubic centimeters:
- Volume = Area x Depth = 720,000,000,000 cm^2 x 1.0 cm^3 = 720,000,000,000 cm^3

5. Convert the volume of water from cubic centimeters to kilograms:
- Mass of water = Volume x 10^-3 kg/cm^3 = 720,000,000,000 cm^3 x 10^-3 kg/cm^3 = 720,000,000 kg

6. Convert the mass of water from kilograms to metric tons:
- Mass of water = 720,000,000 kg x (1 metric ton / 10^3 kg) = 720,000 metric tons

Therefore, approximately 720,000 metric tons of water fell on the city during the 2-hour period.