Chapter 1, Problem 1.48P

Interpretation Introduction

Interpretation:

The length of gauge wire that can be produced from an ore of copper containing $66\text{ \%}$ of copper by mass is to be calculated.

Concept introduction:

Density is defined as mass per unit volume. Mass and volume are physical quantities and the units of mass and volume are fundamental units. Density is the ratio of mass to the volume. The unit of volume is derived from the units of mass and volume. The SI unit of density is ${\text{kg/m}}^{\text{3}}$. The formula to calculate density is,

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

Mass is a physical quantity and its SI unit is kilograms $\left(\text{kg}\right)$. It is the measure of the quantity of the matter present in an object. The other units of mass are grams, milligrams.

Volume is a physical quantity and its SI unit is cubic meter $\left({\text{m}}^{\text{3}}\right)$. The other units of the volume are liter, milliliter, cubic decimeter, microliter.

The formula to calculate the volume of a cylinder is,

$\text{Volume}=\pi r^{2}h$ (1)

Here, $r$ is the radius of the cylinder and $h$ is the height of the cylinder.

The relation between diameter and radius is,

$\text{radius}\left(r\right)=\frac{\text{diameter}\left(d\right)}{2}$ (2)