The area of a circle is approximately what percent of the area of its bounding square?

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Multiple Choice

The area of a circle is approximately what percent of the area of its bounding square?

Explanation:
When a circle fits inside a square (the circle is inscribed in the square), its diameter equals the square’s side. If the side is s, the circle’s radius is r = s/2. The circle’s area is πr^2 = π(s^2)/4, while the square’s area is s^2. The ratio of circle area to square area is (π(s^2)/4) / s^2 = π/4 ≈ 0.7854, which is about 78.54%. So the circle’s area is roughly 78.5% of its bounding square’s area.

When a circle fits inside a square (the circle is inscribed in the square), its diameter equals the square’s side. If the side is s, the circle’s radius is r = s/2. The circle’s area is πr^2 = π(s^2)/4, while the square’s area is s^2. The ratio of circle area to square area is (π(s^2)/4) / s^2 = π/4 ≈ 0.7854, which is about 78.54%. So the circle’s area is roughly 78.5% of its bounding square’s area.

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