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

Options

A. 256 `cm^(2)`
B. 128 `cm^(2)`
C. `sqrt(2)r^(2)`
D. 64 `cm^(2)`

Explanation

To find the area of the square that can be inscribed in a circle of radius 8 cm, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the relationship between the radius of the circle and the diagonal of the square:**
The diagonal of the square is equal to the diameter of the circle. Since the radius of the circle is 8 cm, the diameter (d) will be:
\[ d = 2 \times \text{radius} = 2 \times 8 = 16 \text{ cm} \]

2. **Relate the diagonal of the square to its side length:**
If we denote the side length of the square as \( a \), the relationship between the diagonal \( d \) and the side length \( a \) of the square can be given by the formula:
\[ d = a\sqrt{2} \]
Therefore, we can set up the equation:
\[ 16 = a\sqrt{2} \]

3. **Solve for the side length \( a \):**
To find \( a \), we rearrange the equation:
\[ a = \frac{16}{\sqrt{2}} = 16 \times \frac{\sqrt{2}}{2} = 8\sqrt{2} \text{ cm} \]

4. **Calculate the area of the square:**
The area \( A \) of the square is given by:
\[ A = a^2 = (8\sqrt{2})^2 = 64 \times 2 = 128 \text{ cm}^2 \]

### Final Answer:
The area of the square that can be inscribed in a circle of radius 8 cm is \( 128 \text{ cm}^2 \).

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