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]`

Answer 1

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.