Question

The area of the circle that can be inscribed in a square of side 10 cm is

• A. \(40\pi\ cm^2\)
• B. \(30\pi\ cm^2\)
• C. \(100\pi\ cm^2\)
• D. \(25\pi\ cm^2\)

Answer 1

The Correct Option is D

Given: A square of side 10 cm.

Step 1: Determine the Radius of the Inscribed Circle 

The largest possible circle that can be inscribed in the square will have its diameter equal to the side of the square.

\[ \text{Diameter} = 10 \text{ cm} \] \[ \text{Radius} = \frac{\text{Diameter}}{2} = \frac{10}{2} = 5 \text{ cm} \]

Step 2: Calculate the Area of the Circle

\[ \text{Area} = \pi r^2 = \pi (5)^2 = 25\pi \text{ cm}^2 \]

Final Answer: \(25\pi\) cm²

Answer 2

To find the area of a circle inscribed in a square, follow these steps:

1. Identify the side of the square. Here, the side is 10 cm.

2. For a circle inscribed in a square, the diameter of the circle is equal to the side of the square. Therefore, the diameter \(d\) of the circle is 10 cm.

3. The radius \(r\) of the circle is half of the diameter: \(r = \frac{d}{2}\).

4. Substitute the diameter: \(r = \frac{10}{2} = 5\) cm.

5. The area \(A\) of a circle is given by the formula: \(A = \pi r^2\).

6. Substitute the radius into the formula: \(A = \pi (5)^2 = 25\pi\) cm\(^2\).

7. Therefore, the area of the inscribed circle is \(25\pi\) cm\(^2\).

Thus, the correct answer is: \(25\pi\) cm\(^2\).