To find the surface area of a hemisphere, we need to calculate both the curved surface area and the base area of the hemisphere.
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Curved Surface Area of a Hemisphere: The formula for the curved surface area of a hemisphere is given by: \[ \text{Curved Surface Area} = 2\pi r^2 \] where \( r \) is the radius.
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Base Area of the Hemisphere: The base area, which is a circle, is given by: \[ \text{Base Area} = \pi r^2 \]
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Total Surface Area of the Hemisphere: The total surface area of the hemisphere is the sum of the curved surface area and the base area: \[ \text{Total Surface Area} = \text{Curved Surface Area} + \text{Base Area} = 2\pi r^2 + \pi r^2 = 3\pi r^2 \]
Now, substituting \( r = 10 , \text{m} \): \[ \text{Total Surface Area} = 3\pi (10)^2 = 3\pi \times 100 = 300\pi \]
Thus, the surface area of the hemisphere is: \[ \boxed{300\pi} , \text{m}^2 \]