To calculate the surface area of a sphere with a given diameter, follow these steps:
1. Determine the Radius: The radius is half of the diameter.
[tex]\[
\text{Diameter} = 25 \text{ inches}
\][/tex]
[tex]\[
\text{Radius} = \frac{\text{Diameter}}{2} = \frac{25}{2} = 12.5 \text{ inches}
\][/tex]
2. Use the Formula for Surface Area of a Sphere: The formula for the surface area [tex]\( A \)[/tex] of a sphere is:
[tex]\[
A = 4 \pi r^2
\][/tex]
Where [tex]\( r \)[/tex] is the radius of the sphere.
3. Plug in the Radius:
[tex]\[
A = 4 \pi (12.5)^2
\][/tex]
4. Calculate the Surface Area: When you substitute the radius into the formula and calculate:
[tex]\[
A \approx 1963.5 \text{ square inches}
\][/tex]
Therefore, the surface area of the sphere is [tex]\( 1963.5 \)[/tex] square inches.
So, the correct answer is:
[tex]\[
\boxed{1963.5 \text{ in}^2}
\][/tex]
