Question
The density of sliver is 10.49 g/cm3^3. if a sample of silver has a volume of 0.2 m^3, what is the mass of the sample
Answers
GPT-4o mini
To find the mass of a sample of silver given its density and volume, you can use the formula:
\[
\text{Mass} = \text{Density} \times \text{Volume}
\]
Given:
- Density of silver = \( 10.49 \, \text{g/cm}^3 \)
- Volume of sample = \( 0.2 \, \text{m}^3 \)
First, we need to convert the volume from cubic meters to cubic centimeters, since the density is given in grams per centimeter cubed.
There are \( 1,000,000 \, \text{cm}^3 \) in \( 1 \, \text{m}^3 \), so:
\[
0.2 \, \text{m}^3 = 0.2 \times 1,000,000 \, \text{cm}^3 = 200,000 \, \text{cm}^3
\]
Now we can calculate the mass:
\[
\text{Mass} = 10.49 \, \text{g/cm}^3 \times 200,000 \, \text{cm}^3
\]
\[
\text{Mass} = 2,098,000 \, \text{g}
\]
To convert the mass from grams to kilograms (since \( 1 \, \text{kg} = 1000 \, \text{g} \)):
\[
\text{Mass} = \frac{2,098,000 \, \text{g}}{1000} = 2098 \, \text{kg}
\]
Thus, the mass of the silver sample is **2098 kg**.
\[
\text{Mass} = \text{Density} \times \text{Volume}
\]
Given:
- Density of silver = \( 10.49 \, \text{g/cm}^3 \)
- Volume of sample = \( 0.2 \, \text{m}^3 \)
First, we need to convert the volume from cubic meters to cubic centimeters, since the density is given in grams per centimeter cubed.
There are \( 1,000,000 \, \text{cm}^3 \) in \( 1 \, \text{m}^3 \), so:
\[
0.2 \, \text{m}^3 = 0.2 \times 1,000,000 \, \text{cm}^3 = 200,000 \, \text{cm}^3
\]
Now we can calculate the mass:
\[
\text{Mass} = 10.49 \, \text{g/cm}^3 \times 200,000 \, \text{cm}^3
\]
\[
\text{Mass} = 2,098,000 \, \text{g}
\]
To convert the mass from grams to kilograms (since \( 1 \, \text{kg} = 1000 \, \text{g} \)):
\[
\text{Mass} = \frac{2,098,000 \, \text{g}}{1000} = 2098 \, \text{kg}
\]
Thus, the mass of the silver sample is **2098 kg**.