The volume \( V \) of a sphere can be calculated using the formula:
\[ V = \frac{4}{3} \pi r^3 \]
where \( r \) is the radius of the sphere. Given that the radius \( r = 3 \) yards and using \( \pi \approx 3.14 \), we can substitute these values into the formula:
\[ V = \frac{4}{3} \times 3.14 \times (3)^3 \]
Calculating \( (3)^3 \):
\[ (3)^3 = 27 \]
Now substituting this back into the volume formula:
\[ V = \frac{4}{3} \times 3.14 \times 27 \]
Calculating \( \frac{4}{3} \times 27 \):
\[ \frac{4 \times 27}{3} = \frac{108}{3} = 36 \]
Now substituting back to find \( V \):
\[ V = 36 \times 3.14 \]
Calculating \( 36 \times 3.14 \):
\[ V \approx 113.04 \text{ cubic yards} \]
Therefore, the volume of the sphere is approximately \( 113.04 \) cubic yards.