# 001 A wire of given density and total mass

**Problem 001**

A certain wire that weighs 8.5 g/cc has a total mass of 155 kg.

- What is the density of the wire in kg/m
^{3}? - Find the volume of the wire in cubic centimeter.
- If the total length of the wire is 1500 m, find the cross-sectional area in square millimeters.

**Solution 001**

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Mass density of the wire in kg/m

$\rho = 8.5 \dfrac{\text{g}}{\text{cm}^3} \left( \dfrac{100 \, \text{cm}}{1 \, \text{m}} \right)^3 \left( \dfrac{1 \, \text{kg}}{1000 \, \text{g}} \right)$

^{3}$\rho = 8.5 \dfrac{\text{g}}{\text{cm}^3} \left( \dfrac{100 \, \text{cm}}{1 \, \text{m}} \right)^3 \left( \dfrac{1 \, \text{kg}}{1000 \, \text{g}} \right)$

$\rho = 8 500 \, \text{kg/m}^3$ *answer*

Volume of the wire

$M = \rho V$

$155(1000) = 8.5V$

$V = 18\,235.29 \, \text{ cc}$ *answer*

Cross-sectional area of the wire

$V = AL$

$18\,235.29 = A(1500 \times 100)$

$A = 0.121\,568\,627\,5 \, \text{cm}^2 (10 \, \text{mm} / \text{cm})^2$

$A = 12.16 \, \text{ mm}^2$ *answer*

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