Question

Richard has two circular sprinklers to water his rectangular backyard as shown.

Answer 1

Answer:

109.88 ft² (nearest hundredth)

Step-by-step explanation:

Formulae

• 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)