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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
\[= 14 \times 7 - 2\left( \frac{22}{7} \times 3 . 5 \times 3 . 5 \right)\]
\[ = 98 - 77\]
\[ = 21 {cm}^2\]
Hence, the area of the remaining cardboard is 21 cm2
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