The radius of the cylinder is equal to half the diameter:
[tex]r=\frac{d}{2}=\frac{55.0 mm}{2}=27.5 mm[/tex]
The volume of the cylinder is given by:
[tex]V=\pi r^2 h=\pi (27.5 mm)^2 (54.0 mm)=1.28 \cdot 10^5 mm^3[/tex]
where h is the heigth of the cylinder. Converting into meters,
[tex]V=1.28 \cdot 10^{-4} m^3[/tex]
And the density of the material will be given by the ratio between the mass and the volume:
[tex]d=\frac{m}{V}=\frac{1 kg}{1.28 \cdot 10^{-4} m^3}=7812.5 kg/m^3[/tex]
Taking into account the definition of density and volume of a cylinder, the density of the material is 7.79×10⁻⁶ [tex]\frac{kg}{mm^{3} }[/tex].
Density is defined as the property that matter, whether solid, liquid or gas, has to compress into a given space. So, density is a quantity that allows us to measure the amount of mass in a certain volume of a substance.
Then, the expression for the calculation of density is the quotient between the mass of a body and the volume it occupies:
[tex]density=\frac{mass}{volume}[/tex]
On the other side, the volume of a 3-dimensional solid is the amount of space it occupies. The volume V of a cylinder with radius r is the area of the base B times the height h:
Volume= B×h= π×r²×h
That is, the value of the volume is the number Pi multiplied by the height and the radius squared.
Being the radius of the cylinder equal to half the diameter d, the volume of the cylinder can be calculated as:
Volume= π×[tex](\frac{d}{2})^{2}[/tex]×h
So, in this case, being a cylinder 54.0 mm in height and 55.0 mm in diameter. you know that:
Replacing in the definition of density:
[tex]density=\frac{1 kg}{128,294.79 mm^{3} }[/tex]
Solving:
density= 7.79×10⁻⁶ [tex]\frac{kg}{mm^{3} }[/tex]
In summary, the density of the material is 7.79×10⁻⁶ [tex]\frac{kg}{mm^{3} }[/tex]
Learn more about density:
