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.
Given:
Length of the rectangular cardboard = 14 cm
Breadth of the rectangular cardboard = 7 cm
∵ 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.
25