Density is the mass of a substance that occupies a given volume.
density = `frac(text(mass))(text(volume))`, or D = `frac(M)(V)`
Density is normally measured using units of g/cm3 for smaller amounts, and kg/m3 for larger amounts.
Calculations of density can be represented by a triangle:
To work out the mass, calculate density x volume: to work out density, it is mass ÷ volume, and for volume it is mass ÷ density.
Pressure is a force acting on an area. A force pressing down on a point will exert more pressure than the same force acting over a wide area. Force is measured in Newtons (shown as N) and the area is normally given in square metres.
The formula is Pressure = `frac(text(Force))((Area))`, or P = `frac(F)(A)` and is shown as N/m2, or Nm-2
The formula can also be represented by a triangle:
1. A pair of stiletto heels occupy an area of 2cm2. What is the pressure being applied to a floor if the weight of the woman wearing the stilettos is 560N?
Answer: 280 N/cm2
Unknown is the pressure: using the triangle gives Force ÷ Area = 50 ÷ 2 = 280 N/cm2
2. 4 grams of gold occupy 0.207cm3. What is the density of gold?
Answer: 19.3 g/cm3
Hiding density on the triangle gives mass over volume. 4 ÷ 0.207 = 19.3 g/cm3 to 1 dp.