Question
what finding the surface area of half a sphere what do we multiply by nr^2?
Answers
GPT-4o mini
To find the surface area of a half sphere (also known as a hemisphere), you can use the formula for the surface area of a full sphere and then adjust it for the half sphere.
The surface area \( A \) of a full sphere is given by the formula:
\[
A = 4\pi r^2
\]
For a hemisphere, you must consider both the curved surface area and the base area:
1. The curved surface area of the hemisphere is half that of the full sphere:
\[
\text{Curved surface area} = 2\pi r^2
\]
2. The base area (which is a circle) of the hemisphere is:
\[
\text{Base area} = \pi r^2
\]
To find the total surface area of a hemisphere (including the base), you add the curved surface area and the base area:
\[
\text{Total surface area of hemisphere} = 2\pi r^2 + \pi r^2 = 3\pi r^2
\]
So, when finding the surface area of a hemisphere, you multiply \( \pi r^2 \) by 3.
The surface area \( A \) of a full sphere is given by the formula:
\[
A = 4\pi r^2
\]
For a hemisphere, you must consider both the curved surface area and the base area:
1. The curved surface area of the hemisphere is half that of the full sphere:
\[
\text{Curved surface area} = 2\pi r^2
\]
2. The base area (which is a circle) of the hemisphere is:
\[
\text{Base area} = \pi r^2
\]
To find the total surface area of a hemisphere (including the base), you add the curved surface area and the base area:
\[
\text{Total surface area of hemisphere} = 2\pi r^2 + \pi r^2 = 3\pi r^2
\]
So, when finding the surface area of a hemisphere, you multiply \( \pi r^2 \) by 3.