🤓 Based on our data, we think this question is relevant for Professor Moussa's class at UCF.
The radius of a uniform solid sphere is measured to be (6.50 ± 0.20) cm and its mass is measured to be (1.85 ± 0.02) kg. Determine the density of the sphere in kilograms per cubic meter and the uncertainty in the density.
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:
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