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Select the correct answer.

The diameter of a sphere measures 10.4 inches. What is the surface area of the sphere?

A. [tex]$216.32 \pi \, \text{in}^2$[/tex]
B. [tex]$108.16 \pi \, \text{in}^2$[/tex]
C. [tex][tex]$432.64 \pi \, \text{in}^2$[/tex][/tex]
D. [tex]$54.08 \pi \, \text{in}^2$[/tex]



Answer :

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]