Question

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

Answer 1

Length of the rectangular cardboard = $14cm$ and

Breadth of the rectangular cardboard = $7cm$

Area of cardboard = Area of rectangle = $length\times breadth=14\times 7=98c{m}^2$

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

$2r=7$ or $r=\frac{7}{2}cm$

Again,Area of two circular cut outs =$2\times \pi r^2=2\times \frac{\pi }{7}\times (\frac{7}{2}{)}^2=77c{m}^2$

Now,The area of remaining cardboard = Area of cardboard - Area of two circular cut outs = $98–77=21$

Therefore, area of remaining cardboard is $21c{m}^2$.