Question
find the surface area of the sphere (6mm)
Answers
GPT-4o mini
To find the surface area of a sphere, you can use the formula:
\[
A = 4\pi r^2
\]
where \( A \) is the surface area and \( r \) is the radius of the sphere.
Given the diameter of the sphere is 6 mm, the radius \( r \) is half of the diameter:
\[
r = \frac{diameter}{2} = \frac{6 \, \text{mm}}{2} = 3 \, \text{mm}
\]
Now we can substitute the radius into the surface area formula:
\[
A = 4\pi (3 \, \text{mm})^2
\]
Calculating this:
\[
A = 4\pi (9 \, \text{mm}^2) = 36\pi \, \text{mm}^2
\]
Now, if you want to approximate the value using \( \pi \approx 3.14 \):
\[
A \approx 36 \times 3.14 \, \text{mm}^2 \approx 113.04 \, \text{mm}^2
\]
Therefore, the surface area of the sphere is:
\[
A \approx 36\pi \, \text{mm}^2 \quad \text{or} \quad A \approx 113.04 \, \text{mm}^2
\]
\[
A = 4\pi r^2
\]
where \( A \) is the surface area and \( r \) is the radius of the sphere.
Given the diameter of the sphere is 6 mm, the radius \( r \) is half of the diameter:
\[
r = \frac{diameter}{2} = \frac{6 \, \text{mm}}{2} = 3 \, \text{mm}
\]
Now we can substitute the radius into the surface area formula:
\[
A = 4\pi (3 \, \text{mm})^2
\]
Calculating this:
\[
A = 4\pi (9 \, \text{mm}^2) = 36\pi \, \text{mm}^2
\]
Now, if you want to approximate the value using \( \pi \approx 3.14 \):
\[
A \approx 36 \times 3.14 \, \text{mm}^2 \approx 113.04 \, \text{mm}^2
\]
Therefore, the surface area of the sphere is:
\[
A \approx 36\pi \, \text{mm}^2 \quad \text{or} \quad A \approx 113.04 \, \text{mm}^2
\]