The area of a square is 𝑑. What is the area of the circle which has the…
2018
The area of a square is 𝑑. What is the area of the circle which has the diagonal of the square as its diameter?
Answer: D. 1/2 𝜋𝑑 — Solution: Derive the circle area from the square's area step by step. Let the side length of the square be s. Since the square's area is d, we have s = √d.…
- A.
𝜋𝑑 - B.
𝜋𝑑^2 - C.
1/4 𝜋𝑑^2 - D.
1/2 𝜋𝑑
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Correct answer: D
Solution: Derive the circle area from the square's area step by step.
Let the side length of the square be s. Since the square's area is d, we have s = √d.
The diagonal of the square is s·√2 = √d · √2 = √(2d). This diagonal is the circle's diameter.
Radius of the circle r = (diameter)/2 = √(2d)/2.
Area of the circle = π·r² = π·(√(2d)/2)² = π·(2d)/4 = (1/2)·π·d.
Therefore the area of the circle is (1/2)·π·d.
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