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

Responses

400π m2
400
𝜋

m
2
400 pi m squared

200π m2
200
𝜋

m
2

200 pi m squared

500π m2
500
𝜋

m
2
500 pi m squared

300π m2

1 answer

The surface area \( A \) of a hemisphere can be calculated using the formula:

\[ A = 2\pi r^2 + \pi r^2 \]

Where:

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

For a hemisphere with a radius \( r = 10 , \text{m} \):

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

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

  3. Add both areas to find the total surface area: \[ A = 200\pi + 100\pi = 300\pi , \text{m}^2 \]

Thus, the surface area of the hemisphere is:

\[ \boxed{300\pi , \text{m}^2} \]