Question
Find the surface area of the sphere. Leave your answer in the terms of pi. The diameter is 8 mm.
8 pi
64 pi
32 pi
16 pi
8 pi
64 pi
32 pi
16 pi
Answers
GPT-4o mini
The formula for the surface area \( A \) of a sphere is given by:
\[
A = 4\pi r^2
\]
where \( r \) is the radius of the sphere.
First, we need to find the radius. The radius is half of the diameter. Given that the diameter is 8 mm:
\[
r = \frac{diameter}{2} = \frac{8 \, \text{mm}}{2} = 4 \, \text{mm}
\]
Now we can substitute the radius into the surface area formula:
\[
A = 4\pi (4)^2
\]
Calculating \( (4)^2 \):
\[
(4)^2 = 16
\]
Now substituting back into the surface area formula:
\[
A = 4\pi \cdot 16 = 64\pi
\]
Thus, the surface area of the sphere is:
\[
\boxed{64\pi} \, \text{mm}^2
\]
\[
A = 4\pi r^2
\]
where \( r \) is the radius of the sphere.
First, we need to find the radius. The radius is half of the diameter. Given that the diameter is 8 mm:
\[
r = \frac{diameter}{2} = \frac{8 \, \text{mm}}{2} = 4 \, \text{mm}
\]
Now we can substitute the radius into the surface area formula:
\[
A = 4\pi (4)^2
\]
Calculating \( (4)^2 \):
\[
(4)^2 = 16
\]
Now substituting back into the surface area formula:
\[
A = 4\pi \cdot 16 = 64\pi
\]
Thus, the surface area of the sphere is:
\[
\boxed{64\pi} \, \text{mm}^2
\]