Question

Aluminum is a lightweight metal (density \(=2.70\) \(\mathrm{g} / \mathrm{cm}^{3}\) ) used in aircraft construction, high-voltage transmission lines, and foils. What is its density in \(\mathrm{kg} / \mathrm{m}^{3} ?\)

Short answer

The density of aluminum in kilograms per cubic meter is 2700 kg/m^3.

Step-by-step solution

Conversion of g to kg

We know that 1 g equals 0.001 kg. Since the density of aluminum is 2.70 g/cm^3, this converts to 2.70 * 0.001 kg/cm^3 = 0.0027 kg/cm^3.

Conversion from cm^3 to m^3

In order to convert from cubic centimeters to cubic meters, we must recall that 1 m equals 100 cm. Therefore, (100 cm)^3 = 1,000,000 cm^3 in 1 m^3. Applying this conversion, the density from step 1 becomes 0.0027 * 1,000,000 kg/m^3.

Final Calculation

After multiplying 0.0027 kg/cm^3 by 1,000,000 cm^3/m^3, we get a final density of 2700 kg/m^3.

Key concepts

Aluminum Density

Aluminum is widely known for its lightweight and strong characteristics, making it ideal for industries such as aerospace and construction. Its density is a critical property, essentially measuring how much mass aluminum has in a given volume. In the original exercise, aluminum's density is given as 2.70 grams per cubic centimeter (g/cm³). This means that every cubic centimeter of aluminum weighs 2.70 grams. Understanding this measure is crucial as it influences how aluminum is used in different applications.

Density is a fundamental aspect of materials science because it allows us to understand how a material will behave in various environments. By converting this density into different units, we can better understand and compare its properties in real-world applications.

Unit Conversion

Converting units is a crucial skill in science and engineering that allows for better understanding and communication of measurements. In this exercise, we need to convert the density of aluminum from grams per cubic centimeter (g/cm³) to kilograms per cubic meter (kg/m³).

First, we start by converting grams to kilograms. Since there are 1000 grams in a kilogram, 1 gram equals 0.001 kilograms. Therefore, the density of aluminum, 2.70 g/cm³, is converted to 0.0027 kg/cm³ by multiplying by 0.001.

Understanding unit conversions helps ensure that measurements are accurate and consistent, eliminating errors that might occur from using incorrect units. This is important when dealing with different systems of measurement like metric and imperial systems.

Cubic Meter Conversion

One of the vital steps in solving density conversion problems is converting between different volume units, such as cubic centimeters to cubic meters. This step was addressed in the original solution by recognizing how many cubic centimeters fit into one cubic meter.

Since a meter is 100 centimeters, a cubic meter is equivalent to one million cubic centimeters (1,000,000 cm³). This conversion is necessary because we want the final density of aluminum in kg/m³, which is a standard unit in the metric system.

By applying this conversion, we multiply the density in kg/cm³ by 1,000,000, resulting in 2700 kg/m³. This correct transformation of units helps ensure the results are usable for engineering and scientific applications, providing a clearer insight into material properties.