To find the radius of the cone, 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, and
- \( \pi \) is approximately 3.14.
We are given:
- \( V = 753.6 \) cubic yards,
- \( h = 20 \) yards.
Substituting the values into the volume formula, we have:
\[ 753.6 = \frac{1}{3} \times 3.14 \times r^2 \times 20 \]
First, simplify the equation:
- Calculate \( \frac{1}{3} \times 3.14 \times 20 \):
\[ \frac{1}{3} \times 3.14 \times 20 = \frac{62.8}{3} \approx 20.9333 \]
Now, the equation becomes:
\[ 753.6 = 20.9333 \times r^2 \]
- To find \( r^2 \), divide both sides by 20.9333:
\[ r^2 = \frac{753.6}{20.9333} \approx 35.96 \]
- Now, take the square root to find \( r \):
\[ r \approx \sqrt{35.96} \approx 5.99 \]
Rounding to the nearest hundredth, the radius \( r \) is approximately:
\[ \boxed{5.99} \text{ yards} \]
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