The volume \( V \) of a sphere is given by the formula:
\[ V = \frac{4}{3} \pi r^3 \]
To find the volume of a hemisphere, you simply take half of the volume of the sphere:
\[ V_{\text{hemisphere}} = \frac{1}{2} \left( \frac{4}{3} \pi r^3 \right) = \frac{2}{3} \pi r^3 \]
Given the radius \( r = 10 , \text{m} \), we can substitute this value into the formula:
\[ V_{\text{hemisphere}} = \frac{2}{3} \pi (10)^3 \]
Calculating \( (10)^3 \):
\[ (10)^3 = 1000 \]
So:
\[ V_{\text{hemisphere}} = \frac{2}{3} \pi (1000) = \frac{2000}{3} \pi \]
Now, substituting \( \pi \approx 3.14 \):
\[ V_{\text{hemisphere}} \approx \frac{2000}{3} \times 3.14 \]
Calculating \( \frac{2000}{3} \):
\[ \frac{2000}{3} \approx 666.67 \]
Now multiplying by \( 3.14 \):
\[ V_{\text{hemisphere}} \approx 666.67 \times 3.14 \approx 2093.34 \]
Thus, the volume of the hemisphere is approximately:
\[ \boxed{2093.34} , \text{m}^3 \]