To find 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 the diameter is 3.5 ft, the radius \( r \) is half of the diameter:
\[ r = \frac{3.5}{2} = 1.75 \text{ ft} \]
Now, substitute \( r \) into the volume formula:
\[ V = \frac{4}{3} \cdot 3.14 \cdot (1.75)^3 \]
First, calculate \( (1.75)^3 \):
\[ (1.75)^3 = 1.75 \times 1.75 \times 1.75 \approx 5.359375 \]
Now, plug that value into the volume formula:
\[ V \approx \frac{4}{3} \cdot 3.14 \cdot 5.359375 \]
Now, calculate \( \frac{4}{3} \cdot 3.14 \):
\[ \frac{4}{3} \cdot 3.14 \approx 4.18667 \]
Then multiply that by \( 5.359375 \):
\[ V \approx 4.18667 \cdot 5.359375 \approx 22.421 \text{ ft}^3 \]
Rounding to the nearest hundredth, the volume is:
\[ V \approx 22.42 \text{ ft}^3 \]
So, the closest response is:
22.44 ft.³ (though it is slightly different from our calculation, it's the one that matches the options given).