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). 

 

Answer 1

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

\[= 14 \times 7 - 2\left( \frac{22}{7} \times 3 . 5 \times 3 . 5 \right)\]
\[ = 98 - 77\]
\[ = 21 {cm}^2\]

Hence, the area of the remaining cardboard is 21 cm²