Q. 255.0( 8 Votes )

Two circular pieces of equal radii and maximum area, touching each other are cut out from a rectangular cardboard of dimensions 14 cm × 7 cm. Find the area of the remaining cardboard.

Answer :

Given:

Length of the rectangular cardboard = 14 cm


Breadth of the rectangular cardboard = 7 cm


Ques25.bmp


Area of rectangle = length × breadth


Area of cardboard = 14 × 7 = 98 cm2


Let the two circles with equal radii and maximum area have a radius of ‘r’ cm each.


Then, 2r = 7


r = cm


Area of circle = πr2


Area of two circular cut outs = 2 × πr2


= 2 × × ×


= 11 × 7 = 77 cm2


Thus, the area of remaining cardboard = 98 – 77 = 21 cm2


Hence, the area of remaining cardboard is 21 cm2.


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