Question

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

300π m2
300
𝜋

m
2
300 pi m squared

400π m2
400
𝜋

m
2
400 pi m squared

200π m2
200
𝜋

m
2

200 pi m squared

500π m2

Answer 1

The surface area \( S \) of a hemisphere is given by the formula:

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

This accounts for the curved surface area (\( 2\pi r^2 \)) plus the base area (\( \pi r^2 \)).

Given that the radius \( r = 10 \) m, we can substitute this value into the formula:

\[
S = 2\pi (10)^2 + \pi (10)^2
\]
\[
= 2\pi (100) + \pi (100)
\]
\[
= 200\pi + 100\pi
\]
\[
= 300\pi
\]

Thus, the surface area of the hemisphere is

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