A square is inscribed in a circle with radius 4 inches, how do you find the area of the region inside the circle and outside the square?
(Geometry-Circle)

Created: 1 year ago | Updated: 1 year ago

Updated: 1 year ago

প্রশ্নে বলা হচ্ছে যে, 4 ইঞ্চি ব্যাসার্ধবিশিষ্ট বৃত্তে একটি বর্গ অন্তর্লিখিত রয়েছে। বর্গের বাইরের ও বৃত্তের ভেতরের অংশের ক্ষেত্রফল কত?

Given that, Radius of the circle (r) = 4

So, diameter of the circle $= 2 r = 2 \times 4 = 8$

$∴ A r e a o f t h e c i r c l e = π 4^{2} = 16 π$

Suppose, side of a square = a

$D i a g o n a l o f a s q u a r e = \sqrt{2 a}$

In the figure we can see that,

diagonal of a square = Diagonal of a circle

$S o, \sqrt{2 a} = 8$

$\Rightarrow a = \frac{8}{\sqrt{2}} = 4 \sqrt{2}$

Area of a square $= {(4 \sqrt{2})}^{2} = 32$

∴ The area of the region inside the circle and outside the square = 16π-32. ans.

1 year ago

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