The density of granite is 2.7 g/cm³. What is the weight of a cube, in kg, with a volume of 15 m³?

To find the weight of the cube, we can follow these steps:

### Step 1: Convert the volume from cubic meters to cubic centimeters
The given volume of the cube is \( 15 \, \text{m}^3 \). To convert this to cubic centimeters:
\[
1 \, \text{m}^3 = 1,000,000 \, \text{cm}^3
\]
Thus:
\[
15 \, \text{m}^3 = 15 \times 1,000,000 = 15,000,000 \, \text{cm}^3
\]

### Step 2: Calculate the mass using the density formula
The density \( \rho \) of granite is \( 2.7 \, \text{g/cm}^3 \), and we know the volume \( V = 15,000,000 \, \text{cm}^3 \). The mass \( m \) is given by the formula:
\[
m = \rho \times V
\]
Substituting the values:
\[
m = 2.7 \times 15,000,000 = 40,500,000 \, \text{g}
\]

### Step 3: Convert the mass to kilograms
Since \( 1 \, \text{kg} = 1000 \, \text{g} \), the mass in kilograms is:
\[
\text{Mass} = \frac{40,500,000 \, \text{g}}{1000} = 40,500 \, \text{kg}
\]

### Final Answer:
The weight of the cube is **40,500 kg**.

Would you like further details or have any questions? Here are some related questions for further exploration:

1. What is the mass of a cube with a volume of 1 cubic meter?
2. How does the density of granite compare to other common materials like steel or aluminum?
3. How would the weight change if the material was water instead of granite?
4. If the volume of the cube was halved, what would its new mass be?
5. How is density related to mass and volume in general?

**Tip:** When dealing with density, ensure that all units are consistent (e.g., volume in cm³ for g/cm³ or m³ for kg/m³).

Learn how to calculate the weight of a granite cube with a volume of 15 m³, using the density of granite (2.7 g/cm³). The problem involves unit conversions from cubic meters to cubic centimeters and grams to kilograms, and is suitable for Grades 8-10.

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