The mass of a cubical object is (235.1 ± 0.1) g. If the volume of the object measures (5.25 ± 0.05) cm³, what is its density?

The density of the cubical object is approximately (44.76 ± 0.43) g/cm³. This is calculated by using the mass and volume provided, along with their respective uncertainties. The final density takes into account the combined uncertainties in mass and volume.
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Answered by Anonymous | 2025-07-04

To find the density of the cubical object, we need to divide its mass by its volume. The formula to calculate density ( ρ ) is:
ρ = V m ​
where:

m is the mass of the object,
V is the volume of the object.

Given:

Mass m = 235.1 ± 0.1 g
Volume V = 5.25 ± 0.05 cm³

First, calculate the nominal density:
ρ = 5.25 cm 3 235.1 g ​ ≈ 44.78 g/cm 3
Now, we need to determine the uncertainty in the density. We will use the formula for relative uncertainty, which is given by:
( ρ Δ ρ ​ ) = ( m Δ m ​ ) + ( V Δ V ​ )
where:

Δ ρ is the uncertainty in density,
Δ m = 0.1 g is the uncertainty in mass,
Δ V = 0.05 cm³ is the uncertainty in volume.

Calculate each part:

m Δ m ​ = 235.1 0.1 ​ ≈ 0.000425

V Δ V ​ = 5.25 0.05 ​ ≈ 0.009524


Add the relative uncertainties:
( ρ Δ ρ ​ ) = 0.000425 + 0.009524 = 0.009949
Calculate the absolute uncertainty in density:
Δ ρ = 0.009949 × 44.78 ≈ 0.445
So, the density of the object, with its uncertainty, is:
ρ = 44.78 ± 0.45 g/cm 3
This means that the density of the object is approximately 44.78 g/cm³, with a possible range between 44.33 g/cm³ and 45.23 g/cm³ due to measurement uncertainties.

Answered by ElijahBenjaminCarter | 2025-07-07