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Find the area of the shaded region. Express your answer in terms of \piπ​ and do not round any numbers.

Find the area of the shaded region. Express your answer in terms of \piπ​ and do not-example-1

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7 votes

Answer:

The strategy is to find out the total area and find the area of the 3 circles then subtract the sum of the circles' are from the total area

Total area = (length * width) = ( 3+6+9+12) * 18 = 540 sq. inch

3 Circles area = πr₁² + πr₂² + πr₃²

  • r₁= 12/2 = 6 in
  • r₂ = 9/2 = 4.5 in
  • r₃ = 6/2 = 3 in

πr₁² + πr₂² + πr₃²

π(6²) + π(4.5)² + π(3)²

= 36π + 20.25π + 9π

= 65.25π

Shaded area = 540 - 64.25π = 335.011 sq. in

User VladoDemcak
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