Question 143

# As shown in the figure, there is a square of 24 cm. A circle is inscribed inside the square. Inside the circle are four circles of equal radius which are inscribed. The total area of the shaded region in the figure given below is ________

Solution

The above area can be obtained by the following operation: Area of Big Square - Area of the Bigger circle +Â $$4\times\$$ Area of Smaller Circle +Â $$8\times\$$ Overlapping Area of smaller circles

i) Area of Big Square =Â $$24\times\ 24=576$$

ii) Area of Big circle =Â $$\pi\ 12^2\ =\ 144\pi\$$

iii) Area of smaller circle =Â $$\pi\ 6^2\ =\ 36\pi\$$

iv) For Area of smaller common area = 2b from below figure

Area b = Area of circular arc(2b+a) - Area of triangle (a+b)

= $$\frac{1}{4}\left(36\pi\ \right)-\ \frac{1}{2}\left(6\times\ 6\right)$$Â  =$$9\pi\ -18$$

Area of common part of smaller circle = 2b =Â $$18\pi\ -36$$

Therefore required area = $$576-144\pi+\left(4\times\ 36\pi\right)-8\times\ \left(18\pi\ -36\right)$$

=Â $$288+144\pi\$$Â Â  Â

None of the above are correct

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