3. 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 in units of kg/m^3, we need to convert the mass from grams to kilograms and calculate the volume.
1. Convert mass from grams to kilograms:
Given mass = 10,500 grams
Mass in kilograms = 10,500 grams / 1000 = 10.5 kg
2. Calculate the volume of the cube:
Given side length = 0.65 m
Volume of a cube = side length^3
Volume = 0.65^3 = 0.274625 m^3
3. Calculate density:
Density = Mass / Volume
Density = 10.5 kg / 0.274625 m^3
Density ≈ 38.199 kg/m^3
To find the density of the cube in units of g/mL, we need to convert the volume from m^3 to mL.
1. Convert volume from m^3 to mL:
1 m^3 = 1,000,000 mL
Volume in mL = 0.274625 m^3 * 1,000,000 = 274,625 mL
2. Calculate density:
Density = Mass / Volume
Density = 10,500 grams / 274,625 mL
Density ≈ 0.038 g/mL