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Four circular cardboard pieces of radii $7 cm$ are placed on a paper in such a way that each piece touches the other two pieces. What is the area of the region enclosed between these pieces?

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42

c m^{2}

21

c m^{2}

84

c m^{2}

96

c m^{2}

answer is A.

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Detailed Solution

Given, the radius of each cardboard piece is 7 cm.
These cardboard pieces are placed on a piece of paper in such a way that each piece touches the other two pieces.
Question Image

The diameter of circle =

2 \times 7 = 14

cm.
So, the side of the square is 14cm.
Area of a square is

sid e^{2}

.
Then area of square=

a^{2}

\Rightarrow

Area of square

= (14)^{2}

\Rightarrow

Area of square

= {196 cm}^{2}

Area of quadrant

= \frac{1}{4}

× area of circle.
We know that the area of a circle is 𝜋

r^{2}

, where r is the radius of the circle.
Area of space enclosed by the circles

=

Area of square of side

14

- 4

(Area of quadrant of radius

7

cm) .

\Rightarrow

Area of space enclosed by the circles

= 14^{2} - 4 \times \frac{1}{4} \times \frac{22}{7} \times 7 \times 7

\Rightarrow

Area of space enclosed by the circles

= 196 - 154

\Rightarrow

Area of space enclosed by the circles

= 42 c m^{2}

Hence, option 1 is correct.

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Four circular cardboard pieces of radii 7cm are placed on a paper in such a way that each piece touches the other two pieces. What is the area of the region enclosed between these pieces?

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Four circular cardboard pieces of radii $7 cm$ are placed on a paper in such a way that each piece touches the other two pieces. What is the area of the region enclosed between these pieces?