Problem 4
Question
The density of lead is 11.3 \(\mathrm{g} / \mathrm{cm}^{3} .\) What is this value in kilograms per cubic meter?
Step-by-Step Solution
Verified Answer
The density of lead is 11,300 kg/m³.
1Step 1: Convert Grams to Kilograms
The density given is in grams per cubic centimeter \(11.3\, \text{g/cm}^3\). To convert grams to kilograms, know that 1 gram is \(0.001\) kilograms. Therefore, \(11.3\, \text{g/cm}^3\) becomes \(11.3 \times 0.001 \) kilograms per cubic centimeter, which equals \(0.0113\, \text{kg/cm}^3\).
2Step 2: Convert Cubic Centimeters to Cubic Meters
Since 1 meter is 100 centimeters, \(1 \text{cm}^3\) equals \((1/100)^3 = 1/1,000,000\) cubic meters. Therefore, to convert from \(\text{kg/cm}^3\) to \(\text{kg/m}^3\), multiply the current value \(0.0113 \text{kg/cm}^3\) by \(1,000,000\) to get the density in \(\text{kg/m}^3\).
3Step 3: Calculate the Density in Kilograms per Cubic Meter
By multiplying \(0.0113 \text{kg/cm}^3\) by \(1,000,000\), the result is \(11,300 \text{kg/m}^3\), which is the density of lead in kilograms per cubic meter.
Key Concepts
Unit ConversionDensity CalculationSI Units
Unit Conversion
Unit conversion is the process of converting a measurement from one unit to another. This is essential when dealing with different systems of measurement. Understanding unit conversion helps in recognizing and comparing quantities that might otherwise seem unrelated.
In the given exercise, we began with a density in grams per cubic centimeter and needed to convert it to kilograms per cubic meter. This involved two key conversions: grams to kilograms and cubic centimeters to cubic meters.
To convert from grams to kilograms, remember that 1 gram equals 0.001 kilograms. When converting volumes, knowing that 1 cubic centimeter is equal to 0.000001 cubic meters is crucial. These conversion factors allow us to switch between units seamlessly.
In the given exercise, we began with a density in grams per cubic centimeter and needed to convert it to kilograms per cubic meter. This involved two key conversions: grams to kilograms and cubic centimeters to cubic meters.
To convert from grams to kilograms, remember that 1 gram equals 0.001 kilograms. When converting volumes, knowing that 1 cubic centimeter is equal to 0.000001 cubic meters is crucial. These conversion factors allow us to switch between units seamlessly.
- For mass: Multiply grams by 0.001 to obtain kilograms.
- For volume: Multiply cubic centimeters by 1,000,000 to obtain cubic meters.
Density Calculation
Density is a measure of how much mass is contained in a given volume. It is often expressed in units of mass per unit volume, like grams per cubic centimeter or kilograms per cubic meter.
In the context of the provided exercise, the density of lead is initially given as 11.3 grams per cubic centimeter. To better understand density, it's useful to imagine it as a comparison between how heavy something is and how much space it occupies. A higher density indicates a greater amount of mass packed into a specific space.
When converting density from one unit to another, such as to obtain it in kilograms per cubic meter, calculation adjustments are vital. Here, we first converted the mass units, then the volume units. Keep in mind that the value of the density will appear numerically larger when both the mass unit grows (as in kg) and the volume unit shrinks (as in \(m^3\)).
In the context of the provided exercise, the density of lead is initially given as 11.3 grams per cubic centimeter. To better understand density, it's useful to imagine it as a comparison between how heavy something is and how much space it occupies. A higher density indicates a greater amount of mass packed into a specific space.
When converting density from one unit to another, such as to obtain it in kilograms per cubic meter, calculation adjustments are vital. Here, we first converted the mass units, then the volume units. Keep in mind that the value of the density will appear numerically larger when both the mass unit grows (as in kg) and the volume unit shrinks (as in \(m^3\)).
- Start with the given density value.
- Convert the mass unit (grams to kilograms).
- Convert the volume unit (cubic centimeters to cubic meters).
- Multiply the transformed value to find the new density.
SI Units
SI (International System of Units) is a globally standardized system of measurements, often used in scientific and technical fields. It allows for universal clarity and precision when sharing data and conducting experiments.
In density measurements, the SI unit for mass is the kilogram, and for volume, it is the cubic meter. Therefore, the SI unit for density is expressed in kilograms per cubic meter (\(\text{kg/m}^3\)).
Using SI units in calculations such as density conversion ensures consistency in scientific communication and helps eliminate confusion due to varying measurement systems. Whether you're an engineer designing materials or a chemist solving practical problems, understanding and utilizing SI units is crucial.
In density measurements, the SI unit for mass is the kilogram, and for volume, it is the cubic meter. Therefore, the SI unit for density is expressed in kilograms per cubic meter (\(\text{kg/m}^3\)).
Using SI units in calculations such as density conversion ensures consistency in scientific communication and helps eliminate confusion due to varying measurement systems. Whether you're an engineer designing materials or a chemist solving practical problems, understanding and utilizing SI units is crucial.
- SI units simplify global communication and scientific sharing.
- Kilograms and cubic meters are the SI units for mass and volume, respectively.
- Densities in the SI unit have the format \(\text{kg/m}^3\).
Other exercises in this chapter
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