We're asked to determine the density and its uncertainty for a sphere given its radius and mass.
For operations with uncertainty, we’ll follow two different rules depending on whether we're adding/subtracting or multiplying/dividing:
- When measurements are added or subtracted, sum the absolute or relative uncertainty—the result is the same.
- When measurements are multiplied or divided, sum the relative uncertainties.
So anytime you square a measurement, add the uncertainty twice (three times for a cubed measurement).
To convert between absolute uncertainty and relative uncertainty, we’ll use this formula (m=measurement, Δu=absolute uncertainty):
We'll cover mass and density more in a later video, but you may already know that density is mass over volume, ρ = m/V (ρ is the Greek letter"rho").
The volume of a sphere is given by