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A lawn sprinkler located at the corner of a yard is set to rotate through 115° and project water out 4.1 ft. To three significant digits, what area of lawn is watered by the sprinkler?

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The answer is 16.888 square feet.

To determine the area of the lawn watered by the sprinkler, we can calculate the area of the sector formed by the 115° rotation of the sprinkler. The formula to find the area of a sector is given by:

A = (θ/360°) * π * r^2

Where:

A is the area of the sector.
θ is the central angle of the sector in degrees.
π is a mathematical constant approximately equal to 3.14159.
r is the radius of the sector (the distance the water is projected).
In this case, the central angle θ is 115° and the radius r is 4.1 ft. Let's calculate the area of the sector:

A = (115°/360°) * π * (4.1 ft)^2
A ≈ (0.3194) * (3.14159) * (4.1 ft)^2
A ≈ 0.3194 * 3.14159 * 16.81 ft^2
A ≈ 16.888 ft^2

To three significant digits, the area of the lawn watered by the sprinkler is approximately 16.888 square feet.
User David Dahan
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