The largest possible circle is cut out from a square card-
board. What per cent of the card board will be left?
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Answer:
21.428%
Explanation:
let the side of the square be x
therefore the diameter of the circle is also x
therefore the radius of the circle is x/2
Area of cardboard=x^2sqcm
Area of circle=22/7*(x/2)^2
= 22/7*x^2/4
= 22x^2/28sqcm
Area of left over cardboard=x^2-22x^2/28
=(28x^2-22x^2)/28
=6x^2/28sqcm
=3x^2/14sqcm
percentage of cardboard left= cardboard left /original cardboard area *100
=[(3x^2/14)/x^2] *100
=(3/14)*100. [x^2 gets cancelled in numerator and denominator]
=21.428%
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