A regional telephone company has 15 million subscribers....

A regional telephone company has 15 million subscribers. Each of their telephones is connected to a central office by a copper twisted pair. The average length of these twisted pairs is $10 \mathrm{~km}$. How much is the copper in the local loops worth? Assume that the cross section of each strand is a circle $1 \mathrm{~mm}$ in diameter, the density of copper is $9.0 \mathrm{grams} / \mathrm{cm}^{3}$, and that copper sells for $\$ 6$ per kilogram.

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Key Concepts

Density and Mass Calculation

Density is a material property that relates mass to volume. By multiplying the calculated volume of the material (from its geometric dimensions) by its density, one can determine the total mass of the material. This is a crucial step in processes where the physical properties of materials directly affect their usage and cost.

Economic Cost Estimation

In engineering and economic assessments, estimating the cost of a material involves multiplying its total mass by the price per unit of mass. This principle is fundamental in project budgeting and cost analysis, as it connects physical measurements with financial implications.

Geometry of Cylindrical Wires

This concept involves using the geometric properties of a cylinder to calculate the volume of a wire. The cross-sectional area is determined by the circle’s area formula, and this area is multiplied by the length of the wire to find the total volume. This procedure is a fundamental step in many engineering problems that involve material quantities.

Unit Conversion

Accurate engineering calculations require converting between different units of measurement, such as converting lengths from kilometers to centimeters or masses from grams to kilograms. Making these conversions correctly ensures consistency across the calculation, enabling reliable results.

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