Respuesta :
From the calculations above, the density of the material is 0.01g/mL
To solve this problem, we have to calculate the volume of the cube, but first of all, we should convert the unit from in to cm.
Conversion from Inches to Centimeter
Let us convert the unit of the side length from inches to centimeter.
[tex]\begin{gathered} 1in=2.54\operatorname{cm} \\ 34.16in=\text{xcm} \\ x=34.16\times2.54 \\ x=86.7664\operatorname{cm} \end{gathered}[/tex]Volume of a Cube
The volume of a cube is given as
[tex]\begin{gathered} v=l^3 \\ l=\text{side length} \end{gathered}[/tex]let's substitute the values and solve for the volume.
[tex]\begin{gathered} v=l^3 \\ v=(84.7664)^3 \\ v=653212.87\operatorname{cm}^3 \end{gathered}[/tex]Note;
[tex]\begin{gathered} 1\operatorname{cm}^3=1mL \\ 653212.87\operatorname{cm}^3=653212.87mL \end{gathered}[/tex]Now that we have the volume of the material, let us calculate it's density
Density of a material
The density of a material can be calculated as
[tex]\rho=\frac{\text{mass}}{\text{volume}}[/tex]But the given mass is in kg and we are asked to find the density in g/mL
Conversion of mass from kg to g
[tex]\begin{gathered} 1\operatorname{kg}=1000g \\ 6.85\operatorname{kg}=6850g \end{gathered}[/tex]We can substitute this information and calculate for the density.
[tex]\begin{gathered} \rho=\frac{\text{mass}}{\text{volume}} \\ \rho=\frac{6850}{653212.87} \\ \rho=0.010\text{ g/mL} \end{gathered}[/tex]From the calculations above, the density of the material is 0.01g/mL
