Find the circumference (in cm) of a circle of radius 17.5 cm.

Options

A. 140
B. 110
C. 38
D. 76

Answer

To find the circumference of a circle, we use the formula:

\[ C = 2 \pi r \]

where \( C \) is the circumference, \( \pi \) is a constant (approximately 3.14 or can be taken as \( \frac{22}{7} \) for calculations), and \( r \) is the radius of the circle.

### Step-by-Step Solution:

1. **Identify the given values**:
- Radius \( r = 17.5 \) cm
- Value of \( \pi = \frac{22}{7} \)

2. **Substitute the values into the formula**:
\[ C = 2 \times \pi \times r \]
\[ C = 2 \times \frac{22}{7} \times 17.5 \]

3. **Calculate \( 2 \times \frac{22}{7} \)**:
\[ 2 \times \frac{22}{7} = \frac{44}{7} \]

4. **Now multiply \( \frac{44}{7} \) by \( 17.5 \)**:
- First, convert \( 17.5 \) to a fraction:
\[ 17.5 = \frac{175}{10} = \frac{35}{2} \]
- Now multiply:
\[ C = \frac{44}{7} \times \frac{35}{2} \]

5. **Multiply the fractions**:
\[ C = \frac{44 \times 35}{7 \times 2} \]

6. **Calculate the numerator and denominator**:
- Numerator: \( 44 \times 35 = 1540 \)
- Denominator: \( 7 \times 2 = 14 \)

7. **Now divide the numerator by the denominator**:
\[ C = \frac{1540}{14} \]

8. **Perform the division**:
\[ C = 110 \text{ cm} \]

### Final Answer:
The circumference of the circle is **110 cm**.