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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 other two pieces. Find the area of the portion enclosed Between these pieces.

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.

Answers (1)

[42 cm2]

Solution

Area of shaded portion = Area of square – Area of 4 sectors

            

Radius = 7 cm

Side of square = 14 cm

AB=BC=CD=DA=14 cm           

\therefore ABCD is a square

\thereforeArea of square= 14 \times 14                             (Area of square = (side)2 )

                          =196 cm2

We know that each angle of square =  90^{\circ}

Area of 4 sectors =4 \times \frac{\pi r^{2} \theta}{360}\\

                            \\=\frac{4 \times 7 \times 7 \times 90}{360} \times \frac{22}{7}\\\\ =154 cm^{2}

Area of shaded portion = Area of square – Area of 4 sectors

                                     =196-154=42cm2

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infoexpert24

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