To find the surface area of a hemisphere, we can use the formula:
\[ \text{Surface Area} = 2\pi r^2 + \pi r^2 \]
where \( r \) is the radius of the hemisphere. The first term \( 2\pi r^2 \) calculates the curved surface area, and the second term \( \pi r^2 \) calculates the area of the flat circular base.
Given that the radius \( r = 10 , \text{m} \), we can plug this value into the formula:
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Curved surface area: \[ 2\pi (10)^2 = 2\pi \cdot 100 = 200\pi , \text{m}^2 \]
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Area of the base: \[ \pi (10)^2 = \pi \cdot 100 = 100\pi , \text{m}^2 \]
Now, add both areas together: \[ \text{Total Surface Area} = 200\pi + 100\pi = 300\pi , \text{m}^2 \]
Therefore, the surface area of the hemisphere is: \[ \boxed{300\pi , \text{m}^2} \]
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