he problem is asking for the mass of a sample of mercury given its density and the dimensions of a cylindrical vial containing it.
The formula to calculate the volume of a cylinder is given by:
�
=
�
�
2
ℎ
V=πr2h
where:
( r ) is the radius of the cylinder,
( h ) is the height of the cylinder.
Once we have the volume, we can calculate the mass using the formula:
�
=
�
�
m=ρV
where:
( \rho ) is the density of the substance,
( V ) is the volume.
Given that the density of mercury is 13.6 g/cm³, the radius of the vial is 0.4 cm, and the height of the vial is 5 cm, we can substitute these values into the formulas to find the mass
First, calculate the volume of the cylinder:
r = 0.4 cm
h = 5 cm
V = π(0.4)^2 * 5
V = π(0.16) * 5
V = 0.8π cm³
Now, calculate the mass of the sample of mercury:
ρ = 13.6 g/cm³
m = 13.6 * 0.8π
m ≈ 10.64 g
Therefore, the mass of the sample of mercury is approximately 10.64 grams.