To find the area covered by the sprinkler, we need to use the formula for the area of a circle, which is:
\[ A = \pi r^2 \]
where \( r \) is the radius of the circle.
We know that the circumference (the distance around the circle) is 70 ft. The formula for the circumference of a circle is:
\[ C = 2\pi r \]
We can set this equal to 70 ft to find the radius:
\[ 2\pi r = 70 \]
To solve for \( r \), we divide both sides by \( 2\pi \):
\[ r = \frac{70}{2\pi} = \frac{35}{\pi} \]
Now we can substitute \( r \) back into the area formula:
\[ A = \pi \left( \frac{35}{\pi} \right)^2 \]
Calculating \( r^2 \):
\[ \left( \frac{35}{\pi} \right)^2 = \frac{1225}{\pi^2} \]
Now substituting that into the area formula:
\[ A = \pi \cdot \frac{1225}{\pi^2} = \frac{1225}{\pi} \]
Now, using an approximation for \( \pi \) (approximately 3.14):
\[ A \approx \frac{1225}{3.14} \approx 390.78 \text{ square feet} \]
Thus, the total area that the sprinkler covers is approximately 390.78 square feet.
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