The surface area \( A \) of a hemisphere can be calculated using the formula:
\[ A = 2\pi r^2 + \pi r^2 \]
where \( r \) is the radius of the hemisphere. The first term \( 2\pi r^2 \) is the curved surface area, and the second term \( \pi r^2 \) is the area of the circular base.
For a hemisphere with a radius \( r = 10 , \text{m} \):
-
Calculate \( 2\pi r^2 \): \[ 2\pi (10)^2 = 2\pi (100) = 200\pi \]
-
Calculate the area of the base \( \pi r^2 \): \[ \pi (10)^2 = \pi (100) = 100\pi \]
-
Combine the two areas: \[ A = 200\pi + 100\pi = 300\pi , \text{m}^2 \]
Thus, the surface area of the hemisphere is:
\[ \boxed{300\pi , \text{m}^2} \]