To solve the problem of finding the volume of a sphere with a given diameter, follow these steps:
1. Determine the Radius:
- The diameter of the sphere is given as 8 cm.
- The radius [tex]\( r \)[/tex] of the sphere is half of the diameter.
- Therefore, [tex]\( r = \frac{8}{2} = 4 \)[/tex] cm.
2. Formula for the Volume of a Sphere:
- The volume [tex]\( V \)[/tex] of a sphere is calculated using the formula:
[tex]\[
V = \frac{4}{3} \pi r^3
\][/tex]
3. Substitute the Radius into the Formula:
- Substitute [tex]\( r = 4 \)[/tex] cm into the volume formula:
[tex]\[
V = \frac{4}{3} \pi (4)^3
\][/tex]
4. Calculate the Volume:
- Calculate the cube of the radius:
[tex]\[
4^3 = 64
\][/tex]
- Substitute this value back into the formula:
[tex]\[
V = \frac{4}{3} \pi \times 64
\][/tex]
5. Simplify the Expression:
- Multiply [tex]\(\frac{4}{3}\)[/tex] by 64:
[tex]\[
\frac{4}{3} \times 64 = \frac{256}{3} \approx 85.333
\][/tex]
- Finally, multiply by [tex]\(\pi\)[/tex]:
[tex]\[
V \approx 85.333 \times 3.14159 \approx 268.082573106329
\][/tex]
6. Round to the Nearest Whole Number:
- The result of the volume calculation is approximately 268.082573106329 cm³.
- Rounding this to the nearest whole number, we get 268 cm³.
Therefore, the volume of the sphere is approximately 268 cm³. The correct answer is:
B. 268 cm³.
