Question : The area of the square inscribed in a circle of radius 8 cm is:
Option 1: $256\;\mathrm{cm^2}$
Option 2: $250\;\mathrm{cm^2}$
Option 3: $128\;\mathrm{cm^2}$
Option 4: $125\;\mathrm{cm^2}$
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Correct Answer: $128\;\mathrm{cm^2}$
Solution :
The diagonal of the square is equal to the diameter of the circle.
The diameter of this circle $= 2×8 = 16 \;\mathrm{cm}$
In a square, where the diagonal $(d)$ and the side $(s)$,
$d = s\sqrt{2}$
The side of the square,
$s = \frac{d}{\sqrt{2}} = \frac{16}{\sqrt{2}} = 8\sqrt{2}\;\mathrm{cm}$
$\therefore$ The area of the square inscribed in the circle $=s^2=(8\sqrt{2})^2 = 128\;\mathrm{cm^2}$
Hence, the correct answer is $128\;\mathrm{cm^2}$.
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