Find the circumference of a circle with radius `3.5 cm.`

Answer

To find the circumference of a circle with a radius of 3.5 cm, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the formula for circumference**:
The formula to calculate the circumference (C) of a circle is given by:
\[ C = 2 \pi r \]
where \( r \) is the radius of the circle.

2. **Substitute the given radius**:
Here, the radius \( r \) is given as 3.5 cm. So, we substitute \( r \) in the formula:
\[ C = 2 \pi (3.5) \]

3. **Use the value of π**:
We can use the approximate value of π as \( \frac{22}{7} \) for our calculations. Thus, we can rewrite the formula:
\[ C = 2 \times \frac{22}{7} \times 3.5 \]

4. **Convert 3.5 to a fraction**:
To simplify the multiplication, we can express 3.5 as a fraction:
\[ 3.5 = \frac{35}{10} \]
Now, substituting this into the equation gives:
\[ C = 2 \times \frac{22}{7} \times \frac{35}{10} \]

5. **Simplify the expression**:
Now, we can simplify the multiplication:
- First, calculate \( 2 \times \frac{22}{7} \):
\[ = \frac{44}{7} \]
- Now multiply this by \( \frac{35}{10} \):
\[ C = \frac{44}{7} \times \frac{35}{10} \]

6. **Multiply the fractions**:
To multiply the fractions, multiply the numerators and the denominators:
\[ C = \frac{44 \times 35}{7 \times 10} \]

7. **Calculate the numerator and denominator**:
- The numerator: \( 44 \times 35 = 1540 \)
- The denominator: \( 7 \times 10 = 70 \)
So we have:
\[ C = \frac{1540}{70} \]

8. **Simplify the fraction**:
Now, divide both the numerator and the denominator by 70:
\[ C = 22 \]

9. **Final answer**:
Therefore, the circumference of the circle is:
\[ C = 22 \text{ cm} \]