Each of the questions given below consists of a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statement sufficient to answer the question.
Read both the statements and give answer
What is the area of the circle? (in sq cm)
I The diameter of the circle is 120 cm less than its circumference.
II The diameter of the circle is equal to the side of a square whose perimeter is 224 cm.

Options

A. if the data in statement I alone are sufficient to answer the question, while the data in statement II alone are not sufficient to answer the question.
B. if the data in statement II alone are sufficient to answer the question, while the data in statement I alone are not sufficient to answer the question.
C. if the date in statement I alone or in statement II alone are sufficient to answer the question.
D. if tile data in both the statements I and II are not sufficient to answer the question.

Answer

To solve the question, we need to determine whether the information provided in each statement is sufficient to find the area of the circle. The area of a circle is given by the formula:

\[ \text{Area} = \pi r^2 \]

where \( r \) is the radius of the circle. The diameter \( d \) is related to the radius by the equation:

\[ d = 2r \]

Now, let's analyze each statement step by step.

### Statement I:
"The diameter of the circle is 120 cm less than its circumference."

1. **Understanding the relationship**: The circumference \( C \) of a circle is given by the formula:
\[ C = \pi d \]
Substituting \( d = 2r \), we have:
\[ C = \pi (2r) = 2\pi r \]

2. **Setting up the equation**: According to the statement:
\[ d = C - 120 \]
Substituting the formulas for \( d \) and \( C \):
\[ 2r = 2\pi r - 120 \]

3. **Rearranging the equation**:
\[ 2r - 2\pi r = -120 \]
\[ 2r(1 - \pi) = -120 \]
\[ r(1 - \pi) = -60 \]
Since \( \pi \) is approximately 3.14, \( 1 - \pi \) is negative, which means \( r \) will be positive.

4. **Finding \( r \)**:
\[ r = \frac{-60}{1 - \pi} \]
We can now calculate the area using \( r \).

### Conclusion for Statement I:
Statement I alone is sufficient to find the radius \( r \) and hence the area of the circle.

### Statement II:
"The diameter of the circle is equal to the side of a square whose perimeter is 224 cm."

1. **Finding the side of the square**: The perimeter \( P \) of a square is given by:
\[ P = 4 \times \text{side} \]
Given \( P = 224 \):
\[ 4 \times \text{side} = 224 \]
\[ \text{side} = \frac{224}{4} = 56 \text{ cm} \]

2. **Relating side to diameter**: Since the diameter \( d \) of the circle is equal to the side of the square:
\[ d = 56 \text{ cm} \]

3. **Finding the radius**:
\[ r = \frac{d}{2} = \frac{56}{2} = 28 \text{ cm} \]

4. **Calculating the area**:
\[ \text{Area} = \pi r^2 = \pi (28)^2 = 784\pi \text{ sq cm} \]

### Conclusion for Statement II:
Statement II alone is also sufficient to find the radius \( r \) and hence the area of the circle.

### Final Conclusion:
Both statements I and II are sufficient independently to answer the question about the area of the circle.

### Answer:
The correct option is that each statement alone is sufficient to answer the question.