Chapter 4, Problem 16STP

Interpretation Introduction

Interpretation:

The density of an aluminum cube with sides 2.14 cm and mass 25.1 g needs to be determined. Also, if the density of aluminum is $2.70g/c{m}^3$, percent error should also be calculated.

Concept introduction:

Density is the measure of mass per volume. Percent error is the measurement of the difference between an observed value and a true value.

Answer to Problem 16STP

The observed or calculated density is $2.56g/c{m}^3$ and the percent error is $5.18\%$.

Explanation of Solution

The volume of cube can be calculated as follows:

$Volume=sid{e}^3$

$Volume=2.14cm\times 2.14cm\times 2.14cm=9.80c{m}^3$

Now, density can be calculated from mass and volume as follows:

$Density=\frac{Mass}{Volume}$

$Density=\frac{25.1g}{9.80c{m}^3}=2.56g/c{m}^3$

The given density of aluminium is 2.70 g/cm³.

Thus,

$Percenterror=\frac{(2.70-2.56)}{2.7}=0.0518$

$Percenterror=5.18\%$

Conclusion

Hence, $2.56g/c{m}^3$ is the observed density and $5.18\%$ is the percent error.