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If a Square is Inscribed in a Circle, Find the Ratio of Areas of the Circle and the Square. - CBSE Class 10 - Mathematics

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Question

If a square is inscribed in a circle, find the ratio of areas of the circle and the square.

Solution

Let side of square be x cms inscribed in a circle.

Radius of circle (r) =`1/2`(𝑑𝑖𝑎𝑔𝑜𝑛𝑎𝑙 𝑜𝑓 𝑠𝑞𝑢𝑎𝑟𝑒)

`=1/2(sqrt(2x))`

`=x/sqrt(2)`

Area of square = (side)2 = x2

Area of circle = 𝜋r2

`=pi( x/sqrt(2))^2`

`=(pix^2)/2`

`"Area of circle"/"Area of square"=(pi/2x^2)/x^2=pi/2=pi:2`

 

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Solution If a Square is Inscribed in a Circle, Find the Ratio of Areas of the Circle and the Square. Concept: Areas of Combinations of Plane Figures.
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