Calculating Mass of 1 Cubic Meter of Water in Kilograms

[shimizua]

Homework Statement

Assuming that each cubic centimeter of water has a mass of exactly 1.00 g, find the mass of one cubic meter of water in kilograms.

Homework Equations

well i just changed everything from grams to kilograms and cm to m

The Attempt at a Solution

Well if there is 1g in each cubic centimeter then in 1 meter there is 1g right? so then u just need to convert g to kilograms. but when i do it and enter it into the computer the answer comes up as wrong units and i am entering the units as kg/m^3 is that right. also i got .1kg/m^3 so hopefully that is right also

 

[horatio89]

Actually, 1 cubic centimetre cannot be equal to 1 metre. You see, the former is a unit of volume, and the latter is a unit of length, and they cannot be converted to one another.

Now, picture this... if there the mass of water in a cube of 1cm x 1 cm x 1cm (i.e one cubic centimeter) is 1 g, what is the mass of water in a cube of 1 m x 1m x 1m (i.e. one cubic metre)?

 

[thomate1]

is there any other way to do this
To calculate the mass of one cubic meter of water in kilograms, we must first convert the units from cubic centimeters to cubic meters. This can be done by dividing the volume of one cubic meter (1 m^3) by the volume of one cubic centimeter (1 cm^3). This gives us a conversion factor of 1,000,000 cm^3/m^3.

Next, we can multiply the conversion factor by the mass of one cubic centimeter of water (1 g/cm^3) to get the mass of one cubic meter of water in grams (1,000,000 g/m^3).

Finally, we can convert the units from grams to kilograms by dividing the mass in grams by 1000, giving us a final answer of 1000 kg/m^3.

Therefore, the mass of one cubic meter of water in kilograms is 1000 kg/m^3. It is important to pay attention to units when working with calculations, as incorrect units can lead to incorrect answers. In this case, the units were entered incorrectly as kg/m^3 instead of kg/m^3, resulting in an incorrect answer. By following the correct units and conversion steps, we can accurately calculate the mass of one cubic meter of water in kilograms.