2 questions:

a)Assuming that water has a density of exactly 1 g/cm3 (cubed), find the mass of one cubic meter of water in kilograms.

b)Suppose that it takes 10 hours to drain a container of 5700m3 (cubed) of water. What is the "mass flow rate," in kilograms per second, of water from the container?

a) 1 cubic meter equals 10^6 cm^3.

multiply that by 1.0 g/cm^3 to get the mass in grams. Then convert to kg.

b) 10 hours is 36,000 seconds
5700 m^3 of water has a mass of ___ kg. (Use your answer to part a)

Divide the mass in kg by the time in seconds.

thank you

a) To find the mass of one cubic meter of water in kilograms, we need to use the density of water.

Given:
Density of water = 1 g/cm^3

We know that 1 liter is equal to 1000 cm^3. Therefore, the density can also be expressed as 1 g/mL.

To convert from mL to cubic meter, we need to divide by 1000^3, which is 1,000,000 (since there are 1,000,000 cm^3 in a cubic meter).

So, the mass of one cubic meter of water in kilograms is:
1 g/mL * (1/1,000,000) kg/g = 0.000001 kg

b) The mass flow rate is the amount of mass flowing per unit time.
Given:
Volume of water = 5700 m^3
Time taken to drain the container = 10 hours = 10 * 60 * 60 seconds (since there are 60 seconds in a minute and 60 minutes in an hour)

To find the mass flow rate in kilograms per second, we need to divide the mass of water by the time.

Mass of water = Volume of water * density
Mass of water = 5700 m^3 * 1 g/cm^3 * (1/1,000,000) kg/g = 5.7 kg

Mass flow rate = Mass of water / Time
Mass flow rate = 5.7 kg / (10 * 60 * 60) seconds
Mass flow rate = 5.7 kg / 36000 seconds
Mass flow rate ≈ 0.00015833 kg/s

Therefore, the mass flow rate of water from the container is approximately 0.00015833 kilograms per second.

a) To find the mass of one cubic meter of water in kilograms, we need to multiply the density of water by the volume of water.

The given density of water is 1 g/cm3.

First, let's convert the volume from cubic meters to cubic centimeters, as the density is given in grams per cubic centimeter.

There are 100 centimeters in a meter, so we need to multiply the volume (1 cubic meter) by (100 cm/m)3 to convert it to cubic centimeters:
1 cubic meter = (100 cm/m)3 * 1 cubic meter = 1000000 cm3

Now we can calculate the mass of one cubic meter of water using the density and volume:
Mass = Density * Volume
= 1 g/cm3 * 1000000 cm3
= 1000000 g

To convert grams to kilograms, we divide by 1000:
Mass = 1000000 g / 1000
= 1000 kg

Therefore, the mass of one cubic meter of water is 1000 kilograms.

b) To calculate the mass flow rate in kilograms per second, we need to divide the mass of water (in kilograms) by the time taken (in seconds).

Given:
Volume of water = 5700 m3
Time taken = 10 hours = 10 * 60 * 60 seconds = 36000 seconds

We know that the mass of one cubic meter of water is 1000 kilograms, as calculated in part a).

To find the total mass of water, we multiply the volume by the mass of one cubic meter:
Mass of water = Volume * Mass per cubic meter
= 5700 m3 * 1000 kg/m3
= 5700000 kg

Finally, we divide the mass of water by the time taken to drain it:
Mass flow rate = Mass of water / Time taken
= 5700000 kg / 36000 s
≈ 158.33 kg/s

Therefore, the mass flow rate of water from the container is approximately 158.33 kilograms per second.