Question

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

Answer 1

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`}