To find the surface area of a sphere when given its diameter, we can follow these steps:
1. Calculate the Radius:
The radius ( [tex]\( r \)[/tex] ) is half of the diameter.
[tex]\[
r = \frac{d}{2}
\][/tex]
Given the diameter, [tex]\( d = 10.4 \)[/tex] inches,
[tex]\[
r = \frac{10.4}{2} = 5.2 \text{ inches}
\][/tex]
2. Surface Area Formula:
The surface area [tex]\( S \)[/tex] of a sphere can be calculated using the formula:
[tex]\[
S = 4 \pi r^2
\][/tex]
3. Substitute the Radius:
Plugging the radius [tex]\( r = 5.2 \)[/tex] inches into the formula:
[tex]\[
S = 4 \pi (5.2)^2
\][/tex]
4. Calculate the Surface Area:
First, calculate [tex]\( (5.2)^2 \)[/tex]:
[tex]\[
(5.2)^2 = 27.04
\][/tex]
Then multiply by [tex]\( 4 \pi \)[/tex]:
[tex]\[
S = 4 \pi \times 27.04 = 108.16 \pi
\][/tex]
Therefore, the surface area of the sphere is [tex]\( 108.16 \pi \)[/tex] square inches.
So the correct answer is:
A. [tex]\( 108.16 \pi \)[/tex] in[tex]\(^2\)[/tex]
