Chapter 1, Problem 13STP

To determine

To Define: The term density.

To Find:The density of the material.

Answer to Problem 13STP

$\boxed{\rho =1.5{\text{ g/cm}}^{\text{3}}}$

Explanation of Solution

Given:

Mass of the cube, $m=96\text{ g}$

Edge of the cube, $l=4\text{cm}$

Formula used:

The expression for the volume of a cube is

$V=l^3$........(1)

Here, l is the edge of the cube.

The expression for density of a cube is

$\rho =\frac{m}{V}$........(2)

Here, ρ is the density, m is the mass, and v is the volume.

Calculation:

A measure of mass per unit volume is called density.

Substitute 4cm for lin equation (1).

$\begin{array}{l}V=4\text{ cm}\times 4\text{ cm}\times 4\text{ cm}\\ \boxed{V=64{\text{ cm}}^3}\end{array}$

Substitute $96\text{ g}$ for m and $64{\text{ cm}}^{\text{3}}$ forV in equation (2).

$\begin{array}{l}\rho =\frac{96\text{ g}}{64{\text{ cm}}^{\text{3}}}\\ \boxed{\rho =1.5{\text{ g/cm}}^{\text{3}}}\end{array}$

Conclusion:

Hence, the required density is $\boxed{\rho =1.5{\text{ g/cm}}^{\text{3}}}$ .