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

Richard has two circular sprinklers to water his rectangular backyard as shown.-example-1
User Ina
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1 Answer

5 votes

Answer:

109.88 ft² (nearest hundredth)

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)

User Phonebox
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