Two circular pieces of equal radii and maximum area, touching each oth

1.	Two circular pieces of equal radii and maximum area, touching each other are cut out from a rectangular cardboard of dimensions 14 cm x 7 cm. Find the area of the remaining cardboard.
Answer» Length of the rectangular cardboard = 14 cm and Breadth of the rectangular cardboard = 7 cm Area of cardboard = Area of rectangle = length × breadth = 14 × 7 = 98 cm² Let the two circles with equal radii and maximum area have a radius r each. 2r = 7 or r = 7/2 cm Again, Area of two circular cut outs = 2 × πr² = 2 x 22/7 x (7/2)² = 77 cm² Now, The area of remaining cardboard = Area of cardboard – Area of two circular cut outs = 98 – 77 = 21 Therefore, area of remaining cardboard is 21 cm².

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

Answer»

Length of the rectangular cardboard = 14 cm and

Breadth of the rectangular cardboard = 7 cm

Area of cardboard = Area of rectangle = length × breadth = 14 × 7 = 98 cm²

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

2r = 7 or r = 7/2 cm

Again,

Area of two circular cut outs = 2 × πr²

= 2 x 22/7 x (7/2)²

= 77 cm²

Now,

The area of remaining cardboard = Area of cardboard – Area of two circular cut outs

= 98 – 77

= 21

Therefore, area of remaining cardboard is 21 cm².