Answer:
109.88 ft² (nearest hundredth)
Step-by-step explanation:
<u>Formulae</u>
- Area of a rectangle = width × length
- Area of a circle = πr²
To find the area of the lawn that is not watered, subtract the area of the 2 circles from the area of the rectangle.
From inspection of the diagram
- width of rectangle = 2r
- length of rectangle = 4r
- area = 512 ft²
Substituting the values into the area of a rectangle formula, and solving for r:
⇒ 512 = 2r × 4r
⇒ 512 = 8r²
⇒ r² = 64
⇒ r = ±8
As distance is positive, r = 8 ft
Area of one circle = π8² = 64π ft²
Therefore,
Area not watered = area of rectangle - 2 × area of circle
= 512 - 2(64π)
= 109.88 ft² (nearest hundredth)
