Each question below is followed by two Statements [l] and [II]. You have to determine whether the data given in the statements are sufficient for answering the question. You should use the data and your knowledge of Mathematics to choose between the possible answers. Give answer
What is the radius of the circle?
I. Length of a rectangle is 40% more that these breadth. Area of rectangle is 440 cm Length of rectangle equals to circumference of circle
II. Circumference of circle is equal to side of square having area 484 cm?

Options

A. if the Statement [l] alone is sufficient to answer the question but the Statement [ll] alone is not sufficient
B. if the Statement [II] alone is sufficient to answer the question but the Statement [I] alone is not sufficient
C. if both Statement [I] and [II] together are needed to answer the question
D. if either the Statement [l] alone or Statement [II] alone is sufficient to answer the question

Answer

To solve the problem of determining the radius of the circle based on the provided statements, we will analyze each statement step by step.

### Given Question:
What is the radius of the circle?

### Statement I:
1. **Length of a rectangle is 40% more than its breadth.**
- Let the breadth of the rectangle be \( b \).
- Then, the length \( l \) can be expressed as:
\[ l = b + 0.4b = 1.4b \]

2. **Area of the rectangle is 440 cm².**
- The area \( A \) of the rectangle is given by:
\[ A = l \times b = 440 \]
- Substituting the expression for length:
\[ 1.4b \times b = 440 \]
- This simplifies to:
\[ 1.4b^2 = 440 \]
- Dividing both sides by 1.4:
\[ b^2 = \frac{440}{1.4} = 314.2857 \quad \text{(approximately)} \]
- Taking the square root:
\[ b \approx \sqrt{314.2857} \approx 17.7 \, \text{cm} \]

3. **Finding the length:**
- Now substituting back to find the length:
\[ l = 1.4b \approx 1.4 \times 17.7 \approx 24.78 \, \text{cm} \]

4. **Length of rectangle equals circumference of circle:**
- The circumference \( C \) of the circle is given by:
\[ C = 2\pi r \]
- Setting the length equal to the circumference:
\[ 2\pi r = 24.78 \]
- Solving for \( r \):
\[ r = \frac{24.78}{2\pi} \approx \frac{24.78}{6.2832} \approx 3.94 \, \text{cm} \]

### Statement II:
1. **Circumference of circle is equal to the side of a square having area 484 cm².**
- The area of the square \( A_s \) is given by:
\[ A_s = s^2 = 484 \]
- Taking the square root to find the side \( s \):
\[ s = \sqrt{484} = 22 \, \text{cm} \]

2. **Setting the circumference equal to the side:**
- We know:
\[ C = 22 \, \text{cm} \]
- Using the circumference formula:
\[ 2\pi r = 22 \]
- Solving for \( r \):
\[ r = \frac{22}{2\pi} = \frac{22}{6.2832} \approx 3.5 \, \text{cm} \]

### Conclusion:
Both statements independently provide sufficient information to determine the radius of the circle.

### Final Answer:
The answer is **D**: Each statement alone is sufficient to answer the question.