The surface area \( A \) of a hemisphere can be calculated using the formula:
\[ A = 2\pi r^2 + \pi r^2 \]
This consists of the curved surface area \( 2\pi r^2 \) plus the area of the circular base \( \pi r^2 \).
For a hemisphere with a radius \( r = 10 , \text{m} \):
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Calculate the curved surface area: \[ 2\pi r^2 = 2\pi (10)^2 = 2\pi (100) = 200\pi \]
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Calculate the area of the base: \[ \pi r^2 = \pi (10)^2 = \pi (100) = 100\pi \]
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Combine both parts to find the total surface area: \[ A = 200\pi + 100\pi = 300\pi \]
Thus, the surface area of the hemisphere is:
\[ \boxed{300\pi} , \text{m}^2 \]