Chapter 1, Problem 38A

Solution

Interpretation: Mass of the given figure needs to be determined if a $2c{m}^3$ of the same material has a mass of 4.0 g.

Concept introduction: Mass is a measure of the amount of matter an object contains. It is related to density and volume as follows:

  $\text{Density}=\frac{\text{mass }}{\text{volume}}$

The mass of the cube is 128 g.

Given: $\text{Length}\left(l\right)\text{=Width}\left(w\right)\text{=Height}\left(h\right)=4cm$

Density: Density is defined as mass per unit volume.

  $\text{Density}=\frac{\text{mass }}{\text{volume}}\mathrm{...}\left(i\right)$

After solving the above equation,

  $\text{mass=density×volume}.\mathrm{..}\left(ii\right)$

  $\begin{array}{c}\text{The volume of the cube}=l\times w\times h{\text{ cm}}^3\\ =4\times 4\times 4{\text{ cm}}^3\\ =64{\text{cm}}^3\end{array}$

Now, calculate density

  $\text{Density}=\frac{mass}{volume}=\frac{4\text{g}}{2{\text{cm}}^3}=2\raisebox{1ex}{$\text{g}$}\!\left/ \!\raisebox{-1ex}{${\text{cm}}^{\text{3}}$}\right.$

Now, the mass of the cube $=density\times volume$

  $=2\raisebox{1ex}{$\text{g}$}\!\left/ \!\raisebox{-1ex}{${\text{cm}}^3$}\right.\times 64{\text{cm}}^3$

  $=2\times 64\frac{\text{g}\times {\text{cm}}^3}{{\text{cm}}^3}$

  $=128g$

Thus, the mass of the cube with sides 2 cm is 128 g.