Question

find the surface area of a hemisphere with a radius of 5 m. leave your answer in terms of pi.
- 75 pi
- 25 pi
- 100 pi
- 125 pi
- 40 pi
- 60 pi
- 80 pi

Answer 1

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:

1. Calculate \( 2\pi r^2 \):
\[
2\pi (5^2) = 2\pi (25) = 50\pi
\]

2. Calculate \( \pi r^2 \):
\[
\pi (5^2) = \pi (25) = 25\pi
\]

3. Now, add the two areas together:
\[
\text{Surface Area} = 50\pi + 25\pi = 75\pi
\]

Thus, the surface area of the hemisphere is:

\[
\boxed{75\pi}
\]