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प्रश्न
If a square is inscribed in a circle, find the ratio of the areas of the circle and the square.
उत्तर
If a square is inscribed in a circle, then the diagonals of the square are diameters of the circle.
Let the diagonal of the square be d cm.
Thus, we have:
Radius , `"r" = "d"/2 "cm"`
Area of the circle = πr2
`= pi"d"^2/4 "cm"^2`
We know ;
`"d"= sqrt(2)xx"Side" `
`=> "Side" = ("d"/sqrt(2)) "cm"`
Area of the the circle = πr2
`=pi"d"^2/4 "cm"^2`
We know ;
`d = sqrt(2)xx"side"`
`⇒ "Side" = "d"/sqrt(2) "cm"`
Area of the square`=("Side")^2`
`=("d"/sqrt(2))^2`
`= "d"^2/2 "cm"^2`
Ratio of the area of the circle to that of the square:
`= (pi"d"^2/4)/("d"^2/2)`
`= pi/2 `
Thus, the ratio of the area of the circle to that of the square is π : 2
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