Find the surface area of a hemisphere with a radius 10m. Leave your answer in terms of pi.(1 point)

Question

Responses

500π m2
500 pi m squared

200π m2
200 pi m squared

400π m2
400 pi m squared

300π m2

Answer 1

To find the surface area of a hemisphere with a radius of 10 meters, you need to account for the curved surface and the flat circular base.

1. The curved surface area of a hemisphere is given by the formula: \[ 2\pi r^2 \]
2. The area of the circular base is given by the formula: \[ \pi r^2 \]

Since we need the total surface area, we add these two areas together:

\[
\text{Total Surface Area} = 2\pi r^2 + \pi r^2 = 3\pi r^2
\]

Substitute the given radius (10 meters) into the formula:

\[
3\pi (10)^2 = 3\pi (100) = 300\pi \text{ m}^2
\]

So, the surface area of the hemisphere is \[ 300\pi \text{ m}^2 \].

Therefore, the correct response is:
\[ 300\pi \text{ m}^2 \]