Q: What is the density of a cube of rock, 2 m on a side, if the mass is 16 x 10^3 kg?
A: volume = (2 m)^3 = 8 m^3 so
density = 16 x 10^3 kg/8 m^3 = 2000 kg/m^3
mass = density x volume
Q: What is the mass of a cube of rock that is 2 m on a side and has
a density of 2000 kg/m^3?
A: mass = density x volume = (2000 kg/m^3) x 8 m^3
= 16000 kg.
Q: What is the mass of a cube of rock that is 2 m on a side and has
a density of 3000 kg/m^3?
A: mass = density x volume = (3000 kg/m^3) x 8 m^3
= 24000 kg.
Q: Suppose that you had two cubes of rock, each 2 m on a side and cube A has a density of 2000 kg/m^3 while cube B has a density of 3000 kg/m^3. What is the density of both cubes together. (Note: a better name for an object made of different materials would be "average density.")
A: The total volume is
volume = 8 m^3 + 8 m^3 = 16 m^3
The total mass is
mass = 16000 kg + 24000 kg = 40000 kg
So the density is
density = mass/volume = 40000 kg / 16 m^3
= 2500 kg/m^3.
The density of water is 1000 kg/m^3.
Q: What is the mass of a swimming pool that is 50 m by 20 m by 2 m?
A: mass = density x volume
= (1000 kg/m^3) x ( 50 m x 20 m x 2 m)
= (1000 kg) x (2000 m^3)
= 2 x 10^6 kg.
Q: Why don't people often build swimming pools on the top of buildings?
Davison E. Soper, Institute of Theoretical Science, University of Oregon, Eugene OR 97403 USA soper@bovine.uoregon.edu