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Answer to Q150

ABCD is a square with side a. In centres A,B,C and D four circles are drawn such that each circle touches externally two of the three remaining circles. Let δ be the area interior of the square and exterior of the circles. What is the value of δ?

δ = Shaded area
δ = Area of a square - (4 x ¼ area of a circle)
= a² - (area of a circle)
= a² - πr²
but r = ᵃ⁄₂
= a² - π(ᵃ⁄₂)²
= a² - ((πa²) ÷ 4)
= (4a² - πa²) ÷ 4
= a² [(4 - π) ÷ 4]

Answer: a² [(4 - π) ÷ 4]

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554 viewsNov 22, 2021 at 15:27

Answer to Q150

ABCD is a square with side a. In centres A,B,C and D four circles are drawn such that each circle touches externally two of the three remaining circles. Let δ be the area interior of the square and exterior of the circles. What is the value of δ?

δ = Shaded area
δ = Area of a square - (4 x ¼ area of a circle)
= a² - (area of a circle)
= a² - πr²
but r = ᵃ⁄₂
= a² - π(ᵃ⁄₂)²
= a² - ((πa²) ÷ 4)
= (4a² - πa²) ÷ 4
= a² [(4 - π) ÷ 4]

Answer: a² [(4 - π) ÷ 4]

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