To find the volume 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 from the diameter. The radius is half the diameter:
\[ r = \frac{d}{2} = \frac{3.5 , \text{ft}}{2} = 1.75 , \text{ft} \]
Now we can substitute the radius into the volume formula:
\[ V = \frac{4}{3} \times 3.14 \times (1.75)^3 \]
Next, we calculate \( (1.75)^3 \):
\[ (1.75)^3 = 1.75 \times 1.75 \times 1.75 = 5.359375 \]
Now substituting this value back into the volume formula:
\[ V = \frac{4}{3} \times 3.14 \times 5.359375 \]
Calculating \( \frac{4}{3} \times 3.14 \):
\[ \frac{4}{3} \times 3.14 \approx 4.18666667 \]
Now multiply this value by \( 5.359375 \):
\[ V \approx 4.18666667 \times 5.359375 \approx 22.435 \]
Rounding to the nearest hundredth:
\[ V \approx 22.44 , \text{ft}^3 \]
Therefore, the volume of the sphere is approximately \( \boxed{22.44} , \text{ft}^3 \).