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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