Formula to calculate the uncertainty in the density

GlobalDuty

1. Homework Statement
A radius of a sphere is measured to be (6.45 ± 0.27) cm, and the mass is measured to be (1.78 ± 0.09) kg. Determine the density of the sphere in kilograms per cubic meter and the uncertainty in the density.

2. Homework Equations
Use the following formula to calculate the uncertainty in the density:
Δρ/ρ = Δm/m + 3Δr/r.)

3. The Attempt at a Solution
I already found the density: 1583.62 kg/m3
I just want to know how to get the uncertainty. I don't know how to use the formula given. i always get a really low number with it.

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cepheid

Staff Emeritus
Gold Member
Re: Uncertainty

Welcome to PF!

The uncertainties are the ranges by which the measured quantities can vary, and these ranges are indicated using the symbol 'Delta.' Hence:

Δr = 0.27 cm

Δm = 0.09 kg

and of course, the measured values are:

r = 6.45 cm

m = 1.78 kg

GlobalDuty

Re: Uncertainty

This is what i did after converting to meters:
(0.09/1.78)+(3*.0027/.0645)

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Stonebridge

Re: Uncertainty

0.17614 = Δρ/ρ so you don't need to divide by anything.
To find the actual uncertainty in p you multiply 0.17614 by the density you have calculated.
.

Re: Uncertainty

ok, thank you.

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