To determine the volume of water in a cylindrical container, we start by calculating the total volume of the container and then use the given fraction to find the volume of the water.
1. Identify the given values:
- Base area of the cylinder, [tex]\( A = 100 \, \text{m}^2 \)[/tex]
- Height of the cylinder, [tex]\( h = 12 \, \text{m} \)[/tex]
2. Calculate the total volume of the cylinder:
The formula for the volume [tex]\( V \)[/tex] of a cylinder is given by:
[tex]\[
V = \text{base area} \times \text{height}
\][/tex]
Substituting the given values:
[tex]\[
V = 100 \, \text{m}^2 \times 12 \, \text{m} = 1200 \, \text{m}^3
\][/tex]
3. Determine the volume of the water:
The container is one-third filled with water. Hence, the volume of water [tex]\( V_{\text{water}} \)[/tex] is:
[tex]\[
V_{\text{water}} = \frac{1}{3} \times V
\][/tex]
Substituting the total volume calculated earlier:
[tex]\[
V_{\text{water}} = \frac{1}{3} \times 1200 \, \text{m}^3 = 400 \, \text{m}^3
\][/tex]
Therefore, the volume of the water in the container is [tex]\( \mathbf{400 \, m^3} \)[/tex].
The correct answer is [tex]\( \boxed{400 \, \text{m}^3} \)[/tex].
