Question

A cube with 34.16 inch sides of an unknown material weighs 6.85 kg. What is thismaterial's density in g/mL? (Hint: 1 in = 2.54 cm)

Answer 1

The density of the material is 0.0105g/mL.

1st) We can convert 34.16 inch to cm, knowing that 1 inch is equal to 2.54 cm:

$34.16in\cdot\frac{2.54\operatorname{cm}}{1in}=86.77\operatorname{cm}$

2nd) Now we can calculate the volume of the cube:

$\begin{gathered} \text{Volume}=(length)^3 \\ \text{Volume}=(86.77cm)^3 \\ \text{Volume}=653,294.2\operatorname{cm}^3 \end{gathered}$

3rd) It is necessary to convert 6.85kg into g to calculate the density, so:

$6.85\operatorname{kg}\cdot\frac{1000g}{1\operatorname{kg}}=6850g$

4th) Finally, we can calculate the density of the material using the density formula:

$\begin{gathered} \text{density}=\frac{mass}{volume} \\ \text{density}=\frac{6850g}{653,294.2mL} \\ \text{density}=0.0105g\mathrm{}mL^{-1} \end{gathered}$

Remember that 1cm3 is equal to 1 mL.

So, the density of the material is 0.0105g/mL.