To find the mass of the substance in the container, we need to follow these steps:
1. Convert all measurements to the same unit (centimeters):
- The length is already in centimeters: 30 cm.
- The width is given in millimeters. Converting 50 mm to centimeters:
[tex]\[
50 \, \text{mm} = \frac{50}{10} = 5 \, \text{cm}
\][/tex]
- The height is given in meters. Converting 0.1 m to centimeters:
[tex]\[
0.1 \, \text{m} = 0.1 \times 100 = 10 \, \text{cm}
\][/tex]
2. Calculate the volume of the container in cubic centimeters:
- To find the volume, multiply the length, width, and height:
[tex]\[
\text{Volume} = 30 \, \text{cm} \times 5 \, \text{cm} \times 10 \, \text{cm} = 1500 \, \text{cm}^3
\][/tex]
3. Determine the mass of the substance in grams using the given density:
- The density is given as [tex]\(2.5 \, \text{g/cm}^3\)[/tex].
- Using the formula [tex]\(m = d \times v\)[/tex]:
[tex]\[
\text{Mass} = 2.5 \, \text{g/cm}^3 \times 1500 \, \text{cm}^3 = 3750 \, \text{g}
\][/tex]
4. Convert the mass from grams to kilograms:
- There are 1000 grams in a kilogram:
[tex]\[
3750 \, \text{g} = \frac{3750}{1000} = 3.75 \, \text{kg}
\][/tex]
Therefore, the mass of the substance in the container is [tex]\(3.75 \, \text{kg}\)[/tex].
Among the given options, the correct answer is:
- [tex]\(3.8 \, \text{kg}\)[/tex]
- [tex]\(38 \, \text{kg}\)[/tex]
- [tex]\(380 \, \text{kg}\)[/tex]
- [tex]\(3800 \, \text{kg}\)[/tex]
The closest correct option is:
[tex]\[ 3.8 \, \text{kg} \][/tex]
However, since we have a more accurate value of [tex]\(3.75 \, \text{kg}\)[/tex], we identify that the provided closer answer [tex]\(3.8 \, \text{kg}\)[/tex] is the best choice among the given options.
