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Question
Two circular pieces of equal radii and maximum area, touching each other are cut out from a rectangular card board of dimensions 14 cm × 7 cm. Find the area of the remaining card board. `[\text{Use}pi=22/7]`
Solution
Dimension of the rectangular card board = 14 cm × 7 cm
Since, two circular pieces of equal radii and maximum area touching each other are cut from the rectangular card board, therefore, the diameter of each of each circular piece is 14/2 = 7 cm.
Radius of each circular piece = `7/2`cm
∴ Sum of area of two circular pieces==`2xxpi(7/2)^2=2xx22/7xx49/7=77 cm^2`
Area of the remaining card board = Area of the card board − Area of two circular pieces
= 14 cm × 7 cm − 77 cm2 = 98 cm2 − 77 cm2 = 21 cm2
Thus, the area of the remaining card board is 21 cm2.
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