To find the volume of a sphere given its diameter, we'll follow a step-by-step approach.
1. Calculate the radius:
The radius [tex]\( r \)[/tex] of a sphere is half of its diameter.
[tex]\[
\text{Diameter} = 8 \text{ cm}
\][/tex]
[tex]\[
\text{Radius} = \frac{\text{Diameter}}{2} = \frac{8 \text{ cm}}{2} = 4 \text{ cm}
\][/tex]
2. Use the formula for the volume of a sphere:
The volume [tex]\( V \)[/tex] of a sphere is given by the formula:
[tex]\[
V = \frac{4}{3} \pi r^3
\][/tex]
3. Substitute the radius into the formula:
[tex]\[
V = \frac{4}{3} \times \pi \times (4 \text{ cm})^3
\][/tex]
[tex]\[
V = \frac{4}{3} \times \pi \times 64 \text{ cm}^3
\][/tex]
[tex]\[
V = \frac{256}{3} \times \pi \text{ cm}^3
\][/tex]
4. Calculate the volume using [tex]\( \pi \approx 3.14159 \)[/tex]:
[tex]\[
V \approx \frac{256}{3} \times 3.14159 \text{ cm}^3
\][/tex]
[tex]\[
V \approx 85.3333 \times 3.14159 \text{ cm}^3
\][/tex]
[tex]\[
V \approx 268.08257 \text{ cm}^3
\][/tex]
5. Round the volume to the nearest whole number:
[tex]\[
V \approx 268 \text{ cm}^3
\][/tex]
Therefore, the volume of the sphere, rounded to the nearest whole number, is [tex]\( \boxed{268 \text{ cm}^3} \)[/tex].
By comparing with the given choices, the correct option is:
A. 268 cm³
