To find the surface area of a hemisphere, you 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, \( 2\pi r^2 \), represents the curved surface area, and the second term, \( \pi r^2 \), represents the base area (the circular base).
Given the radius \( r = 5 \) m, we can substitute this into the formula:
-
Calculate \( 2\pi r^2 \): \[ 2\pi (5^2) = 2\pi (25) = 50\pi \]
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Calculate \( \pi r^2 \): \[ \pi (5^2) = \pi (25) = 25\pi \]
-
Now, add the two areas together: \[ \text{Surface Area} = 50\pi + 25\pi = 75\pi \]
Thus, the surface area of the hemisphere is:
\[ \boxed{75\pi} \]