What is the volume when 3.20 kg of copper wires are melted, then cooled into a solid cube? [the density of copper wires is 8.96 g/cm³]

College Physics
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Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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**Question:**

What is the volume when 3.20 kg of copper wires are melted, then cooled into a solid cube?

\[ \text{The density of copper wires is 8.96 g/cm}^3 \]

\[ \_\_\_\_ \text{ cm}^3 \]

**Explanation:**

To find the volume of the copper cube, we need to use the relationship between mass, volume, and density, which is given by the formula:

\[ \text{Density} (\rho) = \frac{\text{Mass} (m)}{\text{Volume} (V)} \]

Rearranging the formula to solve for volume:

\[ \text{Volume} (V) = \frac{\text{Mass} (m)}{\text{Density} (\rho)} \]

Given:
- Mass, \( m = 3.20 \text{ kg} = 3200 \text{ g} \) (since \( 1 \text{ kg} = 1000 \text{ g} \))
- Density, \( \rho = 8.96 \text{ g/cm}^3 \)

Substitute the values into the formula:

\[ V = \frac{3200 \text{ g}}{8.96 \text{ g/cm}^3} \]

\[ V = 357.14 \text{ cm}^3 \]

Therefore, the volume of the copper cube when the 3.20 kg of copper wires are melted and then cooled into a solid cube is approximately 357.14 cm³.
Transcribed Image Text:**Question:** What is the volume when 3.20 kg of copper wires are melted, then cooled into a solid cube? \[ \text{The density of copper wires is 8.96 g/cm}^3 \] \[ \_\_\_\_ \text{ cm}^3 \] **Explanation:** To find the volume of the copper cube, we need to use the relationship between mass, volume, and density, which is given by the formula: \[ \text{Density} (\rho) = \frac{\text{Mass} (m)}{\text{Volume} (V)} \] Rearranging the formula to solve for volume: \[ \text{Volume} (V) = \frac{\text{Mass} (m)}{\text{Density} (\rho)} \] Given: - Mass, \( m = 3.20 \text{ kg} = 3200 \text{ g} \) (since \( 1 \text{ kg} = 1000 \text{ g} \)) - Density, \( \rho = 8.96 \text{ g/cm}^3 \) Substitute the values into the formula: \[ V = \frac{3200 \text{ g}}{8.96 \text{ g/cm}^3} \] \[ V = 357.14 \text{ cm}^3 \] Therefore, the volume of the copper cube when the 3.20 kg of copper wires are melted and then cooled into a solid cube is approximately 357.14 cm³.
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