Two circular pieces of equal radii and maximum area,
Question:

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.

Solution:

We know that we can cut two circular pieces of equal radii and maximum area from the rectangular cardboard whose diameter is equal to the width of the rectangular cardboard.
∴ Radii of two circuar pieces = Half of the width of the rectangular cardboard = 3.5 cm
Now,
Area of remaining cardboard = Area of rectangular cardboard − 2 ⨯ Area of circular piece having radius 3.5 cm

$=14 \times 7-2\left(\frac{22}{7} \times 3.5 \times 3.5\right)$

$=98-77$

$=21 \mathrm{~cm}^{2}$

Hence, the area of the remaining cardboard is 21 cm2