To find the volume of a sphere with a given diameter, we can use the formula for the volume of a sphere:
[tex]\[
V = \frac{4}{3} \pi r^3
\][/tex]
where [tex]\( r \)[/tex] is the radius of the sphere.
First, we need to determine the radius. The radius [tex]\( r \)[/tex] is half of the diameter. Given the diameter is 25 cm, we can find the radius as:
[tex]\[
r = \frac{25}{2} = 12.5 \text{ cm}
\][/tex]
Next, we use the radius to calculate the volume. Plugging in the values into the formula, we get:
[tex]\[
V = \frac{4}{3} \pi (12.5)^3
\][/tex]
Given that [tex]\(\pi \)[/tex] is approximated as 3.14, we can substitute [tex]\(\pi \)[/tex] into the equation:
[tex]\[
V = \frac{4}{3} \times 3.14 \times (12.5)^3
\][/tex]
[tex]\[
V = \frac{4}{3} \times 3.14 \times 1953.125
\][/tex]
[tex]\[
V = \frac{4 \times 3.14 \times 1953.125}{3}
\][/tex]
[tex]\[
V = \frac{24.985 \times 1953.125}{3}
\][/tex]
[tex]\[
V = 8177.083333333333 \text{ cm}^3
\][/tex]
Rounding this to the nearest hundredth, we get:
[tex]\[
V \approx 8177.08 \text{ cm}^3
\][/tex]
Therefore, the volume of the sphere is 8177.08 cm³. Among the provided choices, the best answer is:
[tex]\[
\boxed{8,177.08 \, \text{cm}^3}
\][/tex]
