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?

Answer 1

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