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Question
A circle of the largest area is cut from a rectangular piece of cardboard with dimensions 55 cm and 42 cm. Find the ratio between the area of the circle cut and the area of the remaining card-board.
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Solution
The largest area of the circle is possible when,
diameter = 42
Therefore, radius = `42/2` = 21 cm
Therefore, Area of circle = π × (21)2
= 1386
Area of the rectangle = 55 × 42 = 2310 cm2
Therefore, area of remaining cardboard-
`= 42 xx 55 - pi (21)^2`
`= 42 xx 55 - 22/7 (21)^2`
= 2310 - 1386
= 924
Hence, the volume of the circle and area remaining cardboard-
= 1386 : 924
= 231 : 154
= 3 : 2
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