Questions: The area of the sector is 668.15 square feet.

The area of the sector is 668.15 square feet.
Transcript text: The area of the sector is 668.15 square feet.
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Solution

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Solution Steps

Step 1: Find the area of the sector

The area of a sector of a circle with radius rr and central angle θ\theta (in radians) is given by the formula A=12r2θA = \frac{1}{2}r^2\theta. In this case, the radius is r=20r = 20 feet and the central angle is θ=145∘\theta = 145^\circ. First, convert the angle to radians:

θ=145∘×π180∘=29π36\theta = 145^\circ \times \frac{\pi}{180^\circ} = \frac{29\pi}{36} radians.

Now plug the values into the formula for the area of a sector:

A=12(202)(29π36)=12(400)(29π36)=200(29π36)=5800π36=1450π9A = \frac{1}{2}(20^2)\left(\frac{29\pi}{36}\right) = \frac{1}{2}(400)\left(\frac{29\pi}{36}\right) = 200\left(\frac{29\pi}{36}\right) = \frac{5800\pi}{36} = \frac{1450\pi}{9}

Step 2: Calculate and round

Now calculate the value and round to two decimal places:

A=1450π9≈506.145A = \frac{1450\pi}{9} \approx 506.145

Rounding to two decimal places gives 506.15 square feet.

Final Answer

The area of the lawn that receives water is approximately \\(\boxed{506.15}\\) square feet.

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