A rectangular container measuring 20 cm x 47 cm x 68 cm is filled with water. What is the mass of this volume of water in kilograms and grams?
multiplying the dimensions together will give the volume in cm^3
the density of water is ... 1 gm/cm^3
there are one thousand grams in a kilogram
To find the mass of the water in the container, we need to know the density of water, which is approximately 1 gram per cubic centimeter (g/cm^3) or 1000 kilograms per cubic meter (kg/m^3).
First, let's calculate the volume of the container. The volume of a rectangular container can be calculated by multiplying its length, width, and height. So, the volume (V) of the container is:
V = length x width x height
V = 20 cm x 47 cm x 68 cm
Now, let's convert the volume from cubic centimeters (cm^3) to cubic meters (m^3) since the density of water is given in kilograms per cubic meter.
To convert cubic centimeters to cubic meters, divide the volume by 1,000,000 (since 1 cubic meter is equal to 1,000,000 cubic centimeters).
V(m^3) = V(cm^3) / 1,000,000
Now, we can calculate the mass (M) using the formula:
M = density x volume
Since the density of water is 1000 kg/m^3, we can substitute the values into the formula:
M = 1000 kg/m^3 x V(m^3)
Finally, let's calculate the mass of the water in kilograms:
mass(kg) = 1000 kg/m^3 x V(m^3)
To find the mass in grams, we can multiply the mass in kilograms by 1000:
mass(g) = mass(kg) x 1000
By plugging in the values for the volume, we can find the mass of the water in kilograms and grams.