Question
find the surface area of a sphere with a diameter of 40 inches. Leave your answer in terms of pi.
the surface area is ___ in.^2
the surface area is ___ in.^2
Answers
GPT-4o mini
To find the surface area of a sphere, we use the formula:
\[
\text{Surface Area} = 4\pi r^2
\]
where \( r \) is the radius of the sphere.
Given that the diameter of the sphere is 40 inches, we can find the radius by dividing the diameter by 2:
\[
r = \frac{40}{2} = 20 \text{ inches}
\]
Now we can substitute the radius back into the surface area formula:
\[
\text{Surface Area} = 4\pi (20)^2
\]
\[
= 4\pi \times 400
\]
\[
= 1600\pi \text{ in}^2
\]
Therefore, the surface area is \( \boxed{1600\pi} \) in².
\[
\text{Surface Area} = 4\pi r^2
\]
where \( r \) is the radius of the sphere.
Given that the diameter of the sphere is 40 inches, we can find the radius by dividing the diameter by 2:
\[
r = \frac{40}{2} = 20 \text{ inches}
\]
Now we can substitute the radius back into the surface area formula:
\[
\text{Surface Area} = 4\pi (20)^2
\]
\[
= 4\pi \times 400
\]
\[
= 1600\pi \text{ in}^2
\]
Therefore, the surface area is \( \boxed{1600\pi} \) in².