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2 years ago

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

Mathematics

1 answer:

makvit [3.9K]2 years ago

8 0

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)

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