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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.

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34 cm 2

28 cm 2

21 cm 2

25 c m 2

answer is C.

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Detailed Solution

Given that 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

.
We have to find the area of the remaining cardboard.
The area of a circle can be expressed as

A = π r 2

. Here

r

is the radius of a circle.
Area of the rectangle is,

l × b

, where, l is the length and b is breadth.
The required figure geometry is shown below,
Question Image

It is given that the diameter of the circles is d = 7 cm. Then, the area of the remaining cardboard,

A s

by using the figure geometry is,

A s = l × b − π 4 d 2 + π 4 d 2 ⇒ A s = 14 × 7 − π 4 72 + π 4 72 ⇒ A s = 98 − 77 ⇒ A s = 21 cm 2

The area of the remaining cardboard is

21 cm 2

.
Therefore, the correct option is 3.

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