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  • From each corner of a square of side 4 cm a quadrant of a circle of radius 1 cm is cut and also a circle of diameter 2 cm is cut as shown in Fig. Find the area of the remaining portion of the square.

5. From each corner of a square of side 4 cm a quadrant of a circle of radius 1 cm is cut and also a circle of diameter 2 cm is cut as shown in Fig.  Find the area of the remaining portion of the square.

                    

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Consider the quadrant in the given figure:-  We have an angle of the sector as 90o and radius 1 cm.

    Thus the area of the quadrant is:-

                                                      =\ \frac{90^{\circ}}{360^{\circ}}\times \pi\times 1^2

or                                                   =\ \frac{22}{28}\ cm^2

And the area of the square is :              =\ side^2

                                                =\ 4^2

                                               =\ 16\ cm^2

And, the area of the circle is:-

                                               =\ \pi r^2\ =\ \pi \times 1^2\ =\ \pi\ cm^2

Hence the area of the shaded region is: =    Area of the square   -   Area of the circle   -   4 (Area of quadrant)    

or                                                   =\ 16\ -\ \frac{22}{7}\ -\ 4\left ( \frac{22}{28} \right )

or                                                   =\ \frac{68}{7}\ cm^2

Posted by

Devendra Khairwa

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