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. (Use π = 22/7).
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 $21 \mathrm{~cm}^{2}$