To find the total area that the sprinkler covers, we will use the formula for the area of a circle:
\[ A = \pi r^2 \]
where \( A \) is the area and \( r \) is the radius of the circle.
The problem states that the circumference of the circle is 70 ft. We can use the circumference formula to find the radius:
\[ C = 2 \pi r \]
Setting \( C = 70 \):
\[ 70 = 2 \pi r \]
Now, solve for \( r \):
\[ r = \frac{70}{2 \pi} = \frac{35}{\pi} \]
Next, we can substitute this value of \( r \) back into the area formula:
\[ A = \pi \left(\frac{35}{\pi}\right)^2 \]
Calculating \( r^2 \):
\[ r^2 = \left(\frac{35}{\pi}\right)^2 = \frac{1225}{\pi^2} \]
Now substituting this into the area formula:
\[ A = \pi \cdot \frac{1225}{\pi^2} = \frac{1225}{\pi} \]
To find the total area, we can also calculate this numerically. Using the approximation \( \pi \approx 3.14159 \):
\[ A \approx \frac{1225}{3.14159} \approx 389.69 \text{ ft}^2 \]
Thus, the total area that the sprinkler covers is approximately:
\[ \boxed{389.69 \text{ ft}^2} \]
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