You melt 1 kg of gold into an even-sided cube. What will be the side length of the cube when the density of gold is 19.3 grams/cm?
 
The answer requires 2 decimal places, so
round up!

To find the side length of the cube formed by 1 kg of gold, we will use the formula for the volume of a cube and the fact that:

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

### Given:
- Mass of gold: 1 kg = 1000 grams
- Density of gold: 19.3 g/cm³
- Volume of a cube: \( V = s^3 \) where \( s \) is the side length.

### Steps:
1. Use the formula for density:
   \[
   \text{Volume} = \frac{\text{Mass}}{\text{Density}} = \frac{1000 \, \text{g}}{19.3 \, \text{g/cm}^3}
   \]
   Calculating this:
   \[
   \text{Volume} \approx 51.81 \, \text{cm}^3
   \]

2. Since \( V = s^3 \), solve for \( s \):
   \[
   s = \sqrt[3]{\text{Volume}} = \sqrt[3]{51.81}
   \]

   Calculating the cube root:
   \[
   s \approx 3.73 \, \text{cm}
   \]

So, the side length of the cube is approximately **3.73 cm**.

Would you like more details or have any questions?

### Related questions:
1. What would the side length be if the mass of gold was 2 kg?
2. How does changing the density affect the side length of the cube?
3. What is the volume of a cube with a side length of 4 cm?
4. If the gold is reshaped into a sphere, what would be the radius?
5. How does the volume formula change for different shapes like spheres or cylinders?

**Tip:** Cube roots can be calculated using scientific calculators or cube root functions in most software packages like Excel or Python.

You melt 1 kg of gold into an even-sided cube. What will be the side length of the cube when the density of gold is 19.3 grams/cm³?

Find out how to calculate the side length of a cube made from 1 kg of gold with a density of 19.3 grams/cm³. This solution covers geometry and algebra concepts, including volume and cube root calculations. Suitable for high school students, Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation