To find the surface area of a sphere when the diameter is given, we need to follow these steps:
1. Identify the diameter: Here, the diameter of the sphere is given as 10.4 inches.
2. Calculate the radius: The radius is half of the diameter. Therefore,
[tex]\[
\text{Radius} = \frac{\text{Diameter}}{2} = \frac{10.4 \text{ inches}}{2} = 5.2 \text{ inches}
\][/tex]
3. Surface area formula: 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.
4. Substitute the radius: Plug in the radius into the formula:
[tex]\[
A = 4 \pi (5.2)^2
\][/tex]
5. Calculate the square of the radius: First calculate [tex]\( (5.2)^2 \)[/tex]:
[tex]\[
(5.2)^2 = 27.04
\][/tex]
6. Multiply by 4 and [tex]\(\pi\)[/tex]:
[tex]\[
A = 4 \pi \times 27.04 = 108.16 \pi
\][/tex]
Therefore, the surface area of the sphere is [tex]\( 108.16 \pi \)[/tex] square inches.
The correct answer is:
B. [tex]\( 108.16 \pi \)[/tex] in[tex]\(^2\)[/tex]
