The square’s diagonal equals the circle’s diameter 2r. Area of the square is (1/2) x diagonal² = (1/2) x (2r)² = 2r². Dividing by circle area πr² gives the ratio 2 / π ≈ 0.637.
A square is inscribed in a circle of radius r. Show that the ratio of the area of the square to the area of the circle is equal to 2 / π ≈ 0.637.
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When a square is inscribed in a circle of radius r, the diagonal of the square passes through the centre and equals the diameter of the circle:
Diagonal d = 2r.
Area of the square in terms of its diagonal:
Area(square) = (1/2) x d² = (1/2) x (2r)² = (1/2) x 4r² = 2r².
Area of the circle:
Area(circle) = π x r².
Ratio of the area of the square to the circle:
Ratio = Area(square) / Area(circle) = (2r²) / (πr²) = 2 / π.
Evaluating numerically:
2 / 3.1416 ≈ 0.6366 ≈ 0.637.
Hence proved.
For more NCERT Solutions of Class 9 Ganita Manjari Chapter 6 Measuring Space: Perimeter and Area Question Answer (2026-27)
https://www.tiwariacademy.com/ncert-solutions/class-9/maths/ganita-manjari-chapter-6/