To calculate the mass of the silver sample, we can use the formula:
\[ \text{Mass} = \text{Density} \times \text{Volume} \]
First, we need to ensure that the units of density and volume are compatible. The density of silver is given as \(10.49 , \text{g/cm}^3\), and the volume of the sample is given as \(0.2 , \text{m}^3\).
- Convert the volume from cubic meters to cubic centimeters:
Since \(1 , \text{m}^3 = 1,000,000 , \text{cm}^3\) (or \(1 , \text{m}^3 = 10^6 , \text{cm}^3\)), we convert:
\[ 0.2 , \text{m}^3 = 0.2 \times 1,000,000 , \text{cm}^3 = 200,000 , \text{cm}^3 \]
- Calculate the mass using the density:
Now, we can use the density to find the mass:
\[ \text{Mass} = 10.49 , \text{g/cm}^3 \times 200,000 , \text{cm}^3 \]
Calculating this gives:
\[ \text{Mass} = 10.49 \times 200,000 = 2,098,000 , \text{g} \]
- Convert the mass 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.