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The area of the square that can be inscribed in a circle of radius $8 cm$ is

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128 c m^{2}

256 c m^{2}

64 \sqrt{2} c m^{2}

64 c m^{2}

answer is A.

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Detailed Solution

Given that, a square is inscribed in a circle of radius

8 cm

.
The largest square inscribed in the circle can be expressed as,
The diameter of the circle with radius

8 cm

16 cm

. The diagonal of the square is equal to the diameter of the circle,

AC = 16 cm

.
Determine the side of the square ABCD by using the Pythagoras theorem,

A C 2 = A B 2 + B C 2 ⇒ 162 = 2 A B 2 ⇒ 2562 = A B 2 ⇒ A B 2 = 128

The area of the square is given by (side)

2

.
So, the area of a square

ABCD

is equal to

A B 2 = 128 cm 2

.
Hence the correct option is 1.

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