Question Find the surface area of a hemisphere with a radius 10m. Leave your answer in terms of pi.(1 point) Responses 200π m2 200 pi m squared 500π m2 500 pi m squared 400π m2 400 pi m squared 300π m2 300 pi m squared

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,
• \( 2\pi r^2 \) is the curved surface area,
• \( \pi r^2 \) is the area of the circular base.

For a hemisphere with a radius of \( r = 10 \) m:

1. Calculate the curved surface area: \[ 2\pi (10)^2 = 2\pi (100) = 200\pi , \text{m}^2 \]

2. Calculate the area of the circular base: \[ \pi (10)^2 = \pi (100) = 100\pi , \text{m}^2 \]

3. Add the curved surface area and the base area: \[ \text{Total Surface Area} = 200\pi + 100\pi = 300\pi , \text{m}^2 \]

So, the surface area of the hemisphere is \( \boxed{300\pi , \text{m}^2} \).