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A circle with radius 10 cm is drawn some...

A circle with radius 10 cm is drawn somewhere on a rectangular piece of paper of dimensions `40 cm xx 30 cm.` This paper is kept horizontally on table top and a point is marked on the rectangular paper without seeing towards it. Find the probability that it will marked outside the circle. `("Take "pi=(22)/(7))`

Text Solution

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Area of rectangle `=40xx30 cm^(2) = 1200 cm^(2)`
Area of circle `=pi(10)^(2)=100pi cm^(2)`
`therefore" Area of remaining protion "= (1200-100pi) cm^(2)`
`therefore" Required probability "=("Favourable portion")/("Total portion")=(100(12-pi))/(1200)`
`=(12-(22)/(7))/(12)=(84-22)/(7xx12)=(62)/(7xx12)=(31)/(42)`
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