Chapter 1, Problem 83A

To determine

To Calculate:The volume and density of a rectangular bar.

Answer to Problem 83A

Volume of the rectangular bar is $1.872\times {10}^4{\text{m}}^3$ .

Density of the rectangular bar is $8.8\text{6}{\text{g/cm}}^3$ .

Explanation of Solution

Given:

Length of the rectangular bar, $l=2.347\text{m}$

Thickness of the rectangular bar, $b=3.452\text{cm}$

Height of the rectangular bar, $h=2.31\text{mm}$

Mass of the rectangular bar, $m=1659\text{g}$

Formula Used:

Volume of rectangular bar can be obtained by:

  $V=l\times b\times h$

Where, l is length, b is thickness and his the height.

Density of an object can be obtained by:

  $\rho =\frac{m}{V}$

Where, $\rho$ is the density, m is the mass and V is the volume.

Conversion units:

  $\begin{array}{l}\text{1}\text{cm = 0}\text{.01 m}\\ \text{1 mm = 0}\text{.001 m}\end{array}$

Calculations:

Convert thickness and height in to meters.

  $\begin{array}{l}b=3.452\times 0.01\text{m}\\ b=\text{0}\text{.03452 m}\\ h=\text{2}\text{.31}\times \text{0}\text{.001 m}\\ h=\text{0}\text{.00231 m}\end{array}$

Volume of rectangular bar in cubic meters can be obtained by:

  $\begin{array}{c}V=l\times b\times h\\ =2.347\text{m}\times \text{0}\text{.03452 m}\times \text{0}\text{.00231 m}\\ =1.872\times {10}^{-4}{\text{m}}^3\end{array}$

Density of the rectangular bar in ${\text{g/cm}}^{\text{3}}$ .

  $\begin{array}{c}\rho =\frac{1659\text{g}}{1.872\times {10}^{-4}\times {10}^6{\text{cm}}^3}\\ =8.8\text{6}{\text{g/cm}}^3\end{array}$

Conclusion:

Volume of the rectangular bar is $1.872\times {10}^4{\text{m}}^3$ .

Density of the rectangular bar is $8.8\text{6}{\text{g/cm}}^3$ .