What is the edge length of a cube whose mass for aluminum is 3.44g? Density is 2.70 g/cm3 and Volume = edge length3 %3D O 1.58 cm O 1.07 cm O 2.51 cm O 1.89 cm O 2.01 cm

Chemistry
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ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Chapter1: Chemical Foundations
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### Problem Statement:

**Question:**
What is the edge length of a cube whose mass for aluminum is 3.44g? Density is 2.70 g/cm\(^3\) and Volume = edge length\(^3\).

**Options:**
- 1.58 cm
- 1.07 cm
- 2.51 cm
- 1.89 cm
- 2.01 cm

### Explanation:
To solve this problem, we need to use the relationship between mass, density, and volume. The formula for density is given as:

\[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} \]

Rearranging the formula to solve for volume:

\[ \text{Volume} = \frac{\text{Mass}}{\text{Density}} \]

Given:
- Mass = 3.44 g
- Density = 2.70 g/cm\(^3\)

Substitute the values into the equation:

\[ \text{Volume} = \frac{3.44 \, \text{g}}{2.70 \, \text{g/cm}^3} \]

After calculating the volume, since the volume of the cube is also the cube of the edge length (Volume = edge length\(^3\)), we need to take the cube root of the calculated volume to find the edge length.

### Answer:
Calculate the edge length by following the above steps and choose the correct option from the given choices.

**Correct edge length:**

\[ \text{Edge length} = 1.51 \, \text{cm} \]

So, after solving, the nearest option is 1.58 cm.

### Note:
This kind of problem helps students understand and apply fundamental concepts in physics and mathematics related to density, mass, and volume, fostering critical thinking and problem-solving skills.
Transcribed Image Text:### Problem Statement: **Question:** What is the edge length of a cube whose mass for aluminum is 3.44g? Density is 2.70 g/cm\(^3\) and Volume = edge length\(^3\). **Options:** - 1.58 cm - 1.07 cm - 2.51 cm - 1.89 cm - 2.01 cm ### Explanation: To solve this problem, we need to use the relationship between mass, density, and volume. The formula for density is given as: \[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} \] Rearranging the formula to solve for volume: \[ \text{Volume} = \frac{\text{Mass}}{\text{Density}} \] Given: - Mass = 3.44 g - Density = 2.70 g/cm\(^3\) Substitute the values into the equation: \[ \text{Volume} = \frac{3.44 \, \text{g}}{2.70 \, \text{g/cm}^3} \] After calculating the volume, since the volume of the cube is also the cube of the edge length (Volume = edge length\(^3\)), we need to take the cube root of the calculated volume to find the edge length. ### Answer: Calculate the edge length by following the above steps and choose the correct option from the given choices. **Correct edge length:** \[ \text{Edge length} = 1.51 \, \text{cm} \] So, after solving, the nearest option is 1.58 cm. ### Note: This kind of problem helps students understand and apply fundamental concepts in physics and mathematics related to density, mass, and volume, fostering critical thinking and problem-solving skills.
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