Four circular cardboard pieces of radii 7, cm | vedclass

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Question

Given that, four circular cardboard pieces arc placed on a paper in such a way that each piece touches other two pieces.

Now, we join centre of all

Vedclass · Accepted Answer

$42$

Vedclass · Answer

Given that, four circular cardboard pieces arc placed on a paper in such a way that each piece touches other two pieces.

Now, we join centre of all four circles to each other by a line segment. since, radius of each circle is $7 \,cm$

So, $AB =2 	imes$ Radius of circle

$=2 	imes 7=14 \,cm$

$\Rightarrow$ $A B=B C=C D=A D=14\, cm$

which shows that, quadrilateral $A B C D$ is a square with each of its side is $14\, cm$. We know that, each angle between two adjacent sides of a square is $90^{\circ}$ $	herefore$ Area of sector with $\angle A=90^{\circ}$.

$=\frac{\angle A}{360^{\circ}} 	imes \pi^{2}=\frac{90^{\circ}}{360^{\circ}} 	imes \pi 	imes(7)^{2}$

$=\frac{1}{4} 	imes \frac{22}{7} 	imes 49=\frac{154}{4}=\frac{77}{2}$

$=38.5 cm ^{2}$

$	herefore \quad$ Area of each sector $=4 	imes$ Area of sector with $\angle A$

$=4 	imes 38.5$

$=154\, cm ^{2}$

and area of square $A B C D=$ (side of square)$^{2}$

$=(14)^{2}=196 \,cm ^{2}$ [$	herefore$ area of square $\left.=(	ext { side })^{2}ight]$

So, area of shaded region enclosed between these pieces $=$ Area of square $A B C D$ $-$ Area of each sector

$=196-154$

$=42 \,cm ^{2}$

Hence, required area of the portion enclosed between these pieces is $42 \,cm ^{2}$.

Four circular cardboard pieces of radii $7\, cm$ are placed on a paper in such a way that each piece touches other two pieces. Find the area of the portion enclosed between these pieces. (in $cm^2$)

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