To find the radius of a cone when given its volume, we can use the formula for the volume of a cone:
\[ V = \frac{1}{3} \pi r^2 h \]
Where:
- \( V \) is the volume,
- \( r \) is the radius,
- \( h \) is the height.
Given:
- Volume \( V = 753.6 \) cubic yards,
- Height \( h = 20 \) yards,
- Using \( \pi \approx 3.14 \).
We can rearrange the formula to solve for the radius \( r \):
\[ r^2 = \frac{3V}{\pi h} \]
Now, substituting the known values into the equation:
\[ r^2 = \frac{3 \times 753.6}{3.14 \times 20} \]
Calculating the numerator:
\[ 3 \times 753.6 = 2260.8 \]
Calculating the denominator:
\[ 3.14 \times 20 = 62.8 \]
Now substituting these values back into the equation:
\[ r^2 = \frac{2260.8}{62.8} \]
Calculating \( r^2 \):
\[ r^2 \approx 36 \]
Now, taking the square root to find \( r \):
\[ r \approx \sqrt{36} = 6 \]
Therefore, the radius of the cone is approximately:
\[ \boxed{6.00} \text{ yards} \]