To calculate the volume \( V \) of a sphere, you can use the formula:
\[ V = \frac{4}{3} \pi r^3 \]
where \( r \) is the radius of the sphere.
First, we need to find the radius \( r \) from the diameter \( D \). The radius is half of the diameter:
\[ r = \frac{D}{2} = \frac{10.4 , \text{m}}{2} = 5.2 , \text{m} \]
Now we can substitute \( r \) into the volume formula. Using \( \pi \approx 3.14 \), we have:
\[ V = \frac{4}{3} \times 3.14 \times (5.2)^3 \]
Next, we need to compute \( (5.2)^3 \):
\[ (5.2)^3 = 5.2 \times 5.2 \times 5.2 \]
Calculating step by step:
- \( 5.2 \times 5.2 = 27.04 \)
- \( 27.04 \times 5.2 = 140.608 \)
Now we can substitute \( (5.2)^3 \) back into the volume formula:
\[ V = \frac{4}{3} \times 3.14 \times 140.608 \]
Next, calculate \( 3.14 \times 140.608 \):
\[ 3.14 \times 140.608 \approx 442.07952 \]
Now we multiply by \( \frac{4}{3} \):
\[ V = \frac{4}{3} \times 442.07952 \]
Calculating this gives:
\[ V \approx 589.43936 \]
Finally, rounding to the nearest tenth:
\[ V \approx 589.4 , \text{m}^3 \]
Thus, the volume of the sphere is approximately \( \text{589.4 m}^3 \).