The ratio of circumfgerence and area fo a circle is 2 : 7. What is its circumference ?

Options

A. `14pi`
B. `7/pi`
C. `7pi`
D. `14/pi`

Answer

To solve the problem of finding the circumference of a circle when the ratio of its circumference to its area is given as 2:7, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the formulas**:
- The formula for the circumference (C) of a circle is given by:
\[ C = 2\pi r \]
- The formula for the area (A) of a circle is given by:
\[ A = \pi r^2 \]

2. **Set up the ratio**:
- According to the problem, the ratio of circumference to area is:
\[ \frac{C}{A} = \frac{2}{7} \]

3. **Substitute the formulas into the ratio**:
- Substitute the formulas for circumference and area into the ratio:
\[ \frac{2\pi r}{\pi r^2} = \frac{2}{7} \]

4. **Simplify the ratio**:
- Cancel \(\pi\) from the numerator and denominator:
\[ \frac{2r}{r^2} = \frac{2}{7} \]
- Simplifying further gives:
\[ \frac{2}{r} = \frac{2}{7} \]

5. **Cross-multiply to solve for r**:
- Cross-multiplying gives:
\[ 2 \cdot 7 = 2 \cdot r \]
- This simplifies to:
\[ 14 = 2r \]

6. **Solve for r**:
- Dividing both sides by 2:
\[ r = 7 \]

7. **Calculate the circumference**:
- Now that we have the radius, we can find the circumference:
\[ C = 2\pi r = 2\pi \cdot 7 = 14\pi \]

### Final Answer:
The circumference of the circle is \(14\pi\) cm.

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