You measure a cube and determine that its sides are 0.65m. You place the cube on a mass scale and determine that this cube has a mass of 10,500 grams. What is the density of this cube in units of kg/m3 and in units of g/mL?
To find the density of the cube, we use the formula:
Density = Mass / Volume
First, we need to calculate the volume of the cube. Since all sides are equal, we can use the formula:
Volume = side^3
Given that the side of the cube is 0.65m, the volume is:
Volume = (0.65m)^3 = 0.274625m^3
Next, we convert the mass of the cube from grams to kilograms:
Mass = 10,500 grams = 10.5 kilograms
Now we can calculate the density in units of kg/m^3:
Density = Mass / Volume = 10.5 kg / 0.274625 m^3 ≈ 38.19 kg/m^3
To convert the density to units of g/mL, we need to convert meters to centimeters and kilograms to grams:
1 m = 100 cm
1 kg = 1000 g
So, the volume in cm^3 is:
Volume = 0.274625m^3 × (100 cm / 1 m)^3 ≈ 274,625 cm^3
And the mass in grams is:
Mass = 10.5 kg × (1000 g / 1 kg) = 10,500 g
Finally, we can calculate the density in units of g/mL:
Density = Mass / Volume = 10,500 g / 274,625 cm^3 ≈ 0.0381 g/mL