Question
How to calculate the density of an marble using the mass and volume
Answers
GPT-4o mini
To calculate the density of marble, or any other substance, you can use the following formula:
\[
\text{Density} = \frac{\text{Mass}}{\text{Volume}}
\]
### Steps to Calculate Density:
1. **Measure the Mass**: Use a scale to measure the mass of the marble. Make sure to express it in grams (g) or kilograms (kg) for standard density calculations.
2. **Measure the Volume**:
- If the marble is a regular shape (like a sphere), you can calculate its volume using the formula for that shape. For example, the volume \( V \) of a sphere can be calculated with the formula:
\[
V = \frac{4}{3} \pi r^3
\]
where \( r \) is the radius of the sphere.
- If the marble's shape is irregular, you can determine its volume through water displacement. Fill a graduated cylinder with a known volume of water and note the level. Then, submerge the marble in the water and note the new water level. The volume of the marble is the difference between the two water levels.
3. **Calculate Density**: Once you have both the mass (in grams or kilograms) and the volume (in cubic centimeters for grams or cubic meters for kilograms), plug those values into the density formula.
### Example Calculation:
- **Mass of Marble**: 150 grams
- **Volume of Marble**: 50 cubic centimeters
Using the formula:
\[
\text{Density} = \frac{150 \text{ g}}{50 \text{ cm}^3} = 3 \text{ g/cm}^3
\]
So, the density of the marble would be \( 3 \text{ g/cm}^3 \).
\[
\text{Density} = \frac{\text{Mass}}{\text{Volume}}
\]
### Steps to Calculate Density:
1. **Measure the Mass**: Use a scale to measure the mass of the marble. Make sure to express it in grams (g) or kilograms (kg) for standard density calculations.
2. **Measure the Volume**:
- If the marble is a regular shape (like a sphere), you can calculate its volume using the formula for that shape. For example, the volume \( V \) of a sphere can be calculated with the formula:
\[
V = \frac{4}{3} \pi r^3
\]
where \( r \) is the radius of the sphere.
- If the marble's shape is irregular, you can determine its volume through water displacement. Fill a graduated cylinder with a known volume of water and note the level. Then, submerge the marble in the water and note the new water level. The volume of the marble is the difference between the two water levels.
3. **Calculate Density**: Once you have both the mass (in grams or kilograms) and the volume (in cubic centimeters for grams or cubic meters for kilograms), plug those values into the density formula.
### Example Calculation:
- **Mass of Marble**: 150 grams
- **Volume of Marble**: 50 cubic centimeters
Using the formula:
\[
\text{Density} = \frac{150 \text{ g}}{50 \text{ cm}^3} = 3 \text{ g/cm}^3
\]
So, the density of the marble would be \( 3 \text{ g/cm}^3 \).