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

1 answer

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:

\[ \boxed{75\pi} \]