A square of the largest area is cut out of a circle. What % of the area of the circle is lost as trimmings ?

Explanation

Let the radius of the circle be r units.
`:.` Area of circle `= pi r^(2)` sq. units
Let ABCD be the largest square. ltrbgt `:.` Length of diagonal `= 2r = " side " sqrt2`
side `= (2r)/(sqrt2) = sqrt2r`
`:.` Area (square ABCD) = `("side")^(2) = (sqrt2 r)^(2) = 2r^(2)`
`:.` Area of circle lost by cutting out of a squae of largest area `= 2r^(2)`
`:.` Required percentage of the area of circle lost `= (2r^(2))/(pi r^(2)) xx 100 = (200)/(pi) %`