Question

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

Short answer

Aluminum's density is 2700 kg/m³.

Step-by-step solution

Understanding the Problem

We are given the density of aluminum in \(\mathrm{g}/\mathrm{cm}^3\) and need to convert it to \(\mathrm{kg}/\mathrm{m}^3\).

Conversion Factors Gathering

Identify the conversion factors: \(1\,\mathrm{kg} = 1000\,\mathrm{g}\) and \(1\,\mathrm{m} = 100\,\mathrm{cm}\). Thus, \(1\,\mathrm{m}^3 = (100\,\mathrm{cm})^3 = 1,000,000\,\mathrm{cm}^3\).

Convert Grams to Kilograms

Convert \(2.70\,\mathrm{g}/\mathrm{cm}^3\) to kilograms. This results in \(2.70\, \mathrm{g}/\mathrm{cm}^3 \times \frac{1\,\mathrm{kg}}{1000\,\mathrm{g}} = 0.00270\,\mathrm{kg}/\mathrm{cm}^3\).

Convert Cubic Centimeters to Cubic Meters

Convert the volume unit from cubic centimeters to cubic meters. This involves multiplying \(0.00270\,\mathrm{kg}/\mathrm{cm}^3\) by \(1,000,000\,\mathrm{cm}^3/\mathrm{m}^3\).

Calculate Final Density

Perform the calculation: \(0.00270\,\mathrm{kg}/\mathrm{cm}^3 \times 1,000,000\,\mathrm{cm}^3/\mathrm{m}^3 = 2700\,\mathrm{kg}/\mathrm{m}^3\). This gives the density of aluminum in \(\mathrm{kg}/\mathrm{m}^3\).

Key concepts

Density

Density is a fundamental property of materials, expressing how much mass is contained within a given volume. It helps compare different materials and determine how heavy something feels for its size. Mathematically, density is defined as the mass divided by the volume of an object. For example, if you're given the mass in grams and volume in cubic centimeters, density is calculated as:

• Density = Mass/Volume
• Units: \(\mathrm{g}/\mathrm{cm}^3\)

In our problem, we are dealing with the density of aluminum, a common but highly versatile metal, provided in \(\mathrm{g}/\mathrm{cm}^3\). Understanding density is crucial because it allows us to predict how a material behaves under certain conditions, like floatation and stability.

Aluminum

Aluminum is a widely-used metal known for being lightweight and strong. It's crucial in industries such as

• Aircraft construction
• High-voltage transmission lines
• Beverage cans production
• Packaged food in foils

These uses rely on aluminum's density, which is relatively low at 2.70 \(\mathrm{g}/\mathrm{cm}^3\). This means aluminum is lighter than many metals, making it ideal for applications where weight is a factor. Yet, it retains strength and durability. Understanding its density compared to its size helps in designing and engineering products, optimizing them for performance. Aluminum's properties also make it a perfect candidate for recycling, which benefits the environment too.

Measurement Units

Measurement units are crucial in science and engineering for consistent communication of data. The problem involves converting measurements, which requires knowing how to switch between units used in different contexts. Here are some important conversion factors you need to know:

• 1 kilogram (kg) = 1000 grams (g)
• 1 meter (m) = 100 centimeters (cm)
• Thus, 1 cubic meter (m³) = 1,000,000 cubic centimeters (cm³)

When converting the density of aluminum from \(\mathrm{g}/\mathrm{cm}^3\) to \(\mathrm{kg}/\mathrm{m}^3\), you'll convert both mass and volume units. Being adept with such conversions helps with comparing and analyzing different data since scientific measurements can often be presented in varied units depending on the subject context.

Cubic Meters Conversion

Conversion between different volume units, like cubic centimeters (cm³) and cubic meters (m³), is frequent in science. It's essential for consistency, especially in fields involving engineering calculations and material science. Cubic meters are a larger unit of volume compared to cubic centimeters. The relation is:

• 1 m³ = 1,000,000 cm³

To convert aluminum's density calculation to cubic meters, remember that multiplying by this conversion factor allows the volume in smaller cubic units to scale appropriately. This way, calculations remain accurate when converting density to its equivalent in \(\mathrm{kg}/\mathrm{m}^3\). Such conversions make it easier to apply findings in practical, larger-scale applications, such as constructing structures or manufacturing components. Understanding how to navigate these unit conversions ensures precision and accuracy in real-world applications.