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Found in: Page 16

### Physics For Scientists & Engineers

Book edition 9th Edition
Author(s) Raymond A. Serway, John W. Jewett
Pages 1624 pages
ISBN 9781133947271

# A solid piece of lead has a mass of ${\mathbf{23}}{\mathbf{.}}{\mathbf{94}}{\mathbf{ }}{\mathbf{}}{\mathbf{\text{g}}}$and a volume of ${\mathbf{2}}{\mathbf{.}}{\mathbf{10}}{\mathbf{}}{\mathbf{ }}{{\mathbf{\text{cm}}}}^{{\mathbf{\text{3}}}}$.From these data, calculate the density of lead in SI units (kilograms per cubic meter).

The density of the solid piece of lead in SI unit is $11.4×{\text{10}}^{3} {\text{kg/m}}^{\text{3}}.$

See the step by step solution

## Step 1:Definition and units of density of a substance

The amount of mass of any substance to its quantity or volume gives the density of that substance. Density is defined as the ratio of a mass to the volume of asubstance.

Density is measured inSI unit—$\mathrm{kg}/{\mathrm{m}}^{3}$ andCGS unit—$\mathrm{g}/{\mathrm{cm}}^{3}$

Unit conversion is a conversion of a unit of the same quantity from one unit to another using multiplication or division. It is a multistep process that involves multiplication/division by conversion factor

## Step 2: Expression for the density of a substance and unit conversion

Write the expression for the density of the lead substance in terms of its mass and volume.

$\rho =\frac{m}{V}\dots \dots \text{}\left(1\right)$

Here, $\rho$ is the density of the lead, $m$ is mass of the lead, and $V$ is volume of the lead.

Unit conversion method is used for the density measurements so that the final result will be close to the expected value.

Convert the unit $2.10 {\text{cm}}^{\text{3}}$ for volume $V$ to ${\text{m}}^{\text{3}}$ .

$\begin{array}{rcl}{\text{cm}}^{\text{3}}& =& 1×{10}^{-6}{\text{m}}^{\text{3}}\\ 2.10 {\text{cm}}^{\text{3}}& =& 2.10×{10}^{-6}{\text{m}}^{\text{3}}\end{array}$

Convert the unit $23.94 \text{g}$ for mass $m$ to $kg$.

localid="1663589234857" $\begin{array}{rcl}& & 1 {\text{g = 10}}^{-3} \text{kg}\\ & & 23.94 \text{g =}23.94×{\text{10}}^{-3} \text{kg}\end{array}$

## Step 3: Calculation of density of solid piece of lead in SI units

Replace $23.94 ×{\text{10}}^{-3} \text{kg}$ for $m$ and $2.10 ×10{ }^{-6} {\text{m}}^{\text{3}}$ for $V$ in equation (1).

$\begin{array}{rcl}d\rho & =& \frac{23.94 ×{\text{10}}^{-3} \text{kg}}{2.10 ×10{ }^{-6}{\text{m}}^{\text{3}}}\\ & =& 11.4×{\text{10}}^{3} {\text{kg/m}}^{\text{3}}.\\ & & \end{array}$

Hence, the density of the $\rho$ of the solid piece of lead is $11.4×{\text{10}}^{3} {\text{kg/m}}^{\text{3}}.$