The area of a square that can be inscribed in a circle of radius $8\text{ cm}$ is:
(a) $128\text{ cm}^2$
(b) $256\text{ cm}^2$
(c) $64\text{ cm}^2$
(d) $64\sqrt{2}\text{ cm}^2$
Step-by-Step Solution
Key Concept: Diagonal of inscribed square $=$ Diameter of circle $= 16\text{ cm}$. Side $a = 16/\sqrt{2}$. Area $= a^2 = 256/2 = 128\text{ cm}^2$.
Diagonal $= 16\text{ cm} \Rightarrow \text{Area} = \dfrac{\text{Diagonal}^2}{2} = \dfrac{256}{2} = 128\text{ cm}^2$. [1.0 Mark]
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Calculating area $= 128\text{ cm}^2$: 1.0 Mark
Correct Answer: $128\text{ cm}^2$