A square of diagonal 8cm is inscribe in a circle. Find the area of remaining part of circle?

A square of diagonal 8cm is inscribe in a circle. Find the area of rem

1.	A square of diagonal 8cm is inscribe in a circle. Find the area of remaining part of circle?
Answer» We know that diagonal of square of side a={tex}\\sqrt 2\\ a{/tex}{tex}\\Rightarrow{/tex}\xa08={tex}\\sqrt 2\\ a{/tex}{tex}\\Rightarrow\\ a=4\\sqrt 2{/tex}Area of square={tex}(4\\sqrt2)^2=32{/tex}Diameter of a circle = Diagonal of a square = 8cm{tex} \\Rightarrow {/tex}\xa0Radius of a circle = 4cmArea of required region= Area of a circle - Area of a square{tex} = \\left[ {\\pi {{(4)}^2} - 32} \\right]c{m^2}{/tex}{tex} = \\left( {16\\pi - 32} \\right)c{m^2}{/tex}