To calculate the volume of a sphere, you can use the formula:
\[ V = \frac{4}{3} \pi r^3 \]
where \( V \) is the volume and \( r \) is the radius of the sphere.
Given that the diameter of the sphere is 12 cm, we first find the radius:
\[ r = \frac{diameter}{2} = \frac{12 , \text{cm}}{2} = 6 , \text{cm} \]
Now, we can substitute \( r = 6 \) cm into the volume formula:
\[ V = \frac{4}{3} \pi (6 , \text{cm})^3 \]
Calculating \( (6 , \text{cm})^3 \):
\[ (6 , \text{cm})^3 = 6 \times 6 \times 6 = 216 , \text{cm}^3 \]
Now substituting this back into the volume formula:
\[ V = \frac{4}{3} \pi (216 , \text{cm}^3) \]
Using \( \pi \approx 3.14 \):
\[ V = \frac{4}{3} \times 3.14 \times 216 \]
Calculating \( \frac{4}{3} \times 216 \):
\[ \frac{4 \times 216}{3} = \frac{864}{3} = 288 \]
Now multiplying by 3.14:
\[ V \approx 288 \times 3.14 = 904.32 , \text{cm}^3 \]
Rounding to the nearest tenth:
\[ V \approx 904.3 , \text{cm}^3 \]
Therefore, the volume of the sphere is approximately 904.3 cm³.