Question

An aluminum lid has a mass of \(6.5 \mathrm{~g}\). It has a volume of \(2.4 \mathrm{~cm}^{3}\). Calculate the density of aluminum in grams per cubic centimeter.

Short answer

The density of aluminum is approximately \(2.71\, \text{g/cm}^3\).

Step-by-step solution

Understand the formula for density

Density is calculated using the formula: \( \text{Density} = \frac{\text{Mass}}{\text{Volume}} \). This formula tells us that density is the mass of the object divided by its volume.

Identify the given values

From the problem, we know the mass of the aluminum lid is given as \(6.5\, \text{g}\) and the volume is \(2.4\, \text{cm}^{3}\). These are the values we will use in our density formula.

Plug in the values into the formula

Substitute the given values into the density formula: \( \text{Density} = \frac{6.5\, \text{g}}{2.4\, \text{cm}^{3}} \).

Calculate the density

Perform the division: \( \text{Density} = \frac{6.5}{2.4} \approx 2.7083 \). Therefore, the density of aluminum is approximately \(2.7083\, \text{g/cm}^{3}\).

Round the final result

Since we typically express density to two decimal places, round \(2.7083\) to \(2.71\). Thus, the density is approximately \(2.71\, \text{g/cm}^{3}\).

Key concepts

aluminum density

Density is a fundamental property of matter that relates mass with volume. When talking about aluminum density, we refer to how much mass is contained within a given volume of this metal. In practical terms, knowing the density of aluminum helps us understand how heavy a piece of aluminum will be for its size. In our exercise, we calculated the density of an aluminum lid. Aluminum is known for having a moderate density, which makes it suitable for many applications where strength and lightweight properties are necessary. Generally, the accepted value for aluminum density is approximately 2.70 g/cm³, which aligns well with the result we obtained in our problem. This consistency is important as it ensures that our calculations reflect the true characteristics of aluminum.

mass and volume

The concepts of mass and volume are crucial when calculating density. Let's break down what these terms mean:

• Mass: Mass is how much matter is in an object. For our aluminum lid, the mass was given as 6.5 grams.
• Volume: Volume indicates how much space an object occupies. Our aluminum lid had a volume of 2.4 cm³.

Understanding how to measure mass and volume is vital because these measurements allow us to use the density formula effectively. In laboratory conditions, mass is typically measured using scales or balances, while volume can be determined through geometric calculations or by displacement methods. The coherence between mass and volume gives rise to the concept of density.

density formula

The density formula is a simple yet powerful mathematical tool used to calculate the amount of mass per unit volume. The formula is expressed as:\[ \text{Density} = \frac{\text{Mass}}{\text{Volume}}\]This direct relationship shows us that density increases with more mass or less volume. If the volume goes up without a change in mass, the density decreases, and vice versa.In our exercise, we used the given mass of 6.5 grams and the volume of 2.4 cm³. Plugging these into the formula provided us with the numerical density value. It's crucial always to have the mass and volume in compatible units; otherwise, the density value will not be accurate. Converting the units before plugging them into the formula can save many headaches and lead to precise results.

step-by-step calculation

Completing any calculation involves a methodical approach, and our problem was no different. A step-by-step method helps clarify each part of the process, ensuring accuracy and understanding.Here's a recap of the steps:1. **Understand the Formula:** Familiarize yourself with the density formula \[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} \].2. **Identify Given Values:** Before any calculation, ensure you know the mass and volume values. In our exercise, these were 6.5 g and 2.4 cm³ respectively.3. **Perform the Calculation:** Substitute the known values into the density formula, perform the division, and calculate the outcome.4. **Round the Result:** To keep results practical, always round numbers to a reasonable decimal place, often two for density, giving an answer like 2.71 g/cm³.By following each step carefully, we demystify the process and ensure we reach an accurate and reliable answer.