To solve this problem, we need to calculate the total surface area of the spherical orange and then determine the surface area for one of its four equal sections.
### Step 1: Calculate the total surface area of the sphere
The formula for the surface area \(A\) of a sphere is given by:
[tex]\[ A = 4 \pi r^2 \][/tex]
where \(r\) is the radius of the sphere.
Given that the radius \(r\) is 4 centimeters, we can substitute this value into the formula to find the total surface area.
[tex]\[
A = 4 \pi (4)^2
\][/tex]
[tex]\[
A = 4 \pi \times 16
\][/tex]
[tex]\[
A = 64 \pi \text{ square centimeters}
\][/tex]
### Step 2: Calculate the surface area of one slice
Since the orange is split into four equal sections, each section will have one-fourth of the total surface area.
[tex]\[
\text{Surface area of one slice} = \frac{64 \pi}{4}
\][/tex]
[tex]\[
\text{Surface area of one slice} = 16 \pi \text{ square centimeters}
\][/tex]
Thus, the surface area of one slice of the orange is \(16 \pi \) square centimeters. Therefore, the correct answer is:
[tex]\[ 16 \pi \text{ cm}^2 \][/tex]
