Find the radius of a circle whose circumference is 57.2 cm.

Options

A. `5.1cm`
B. `6.1cm`
C. `9.1cm`
D. `8.1cm`

Answer

To find the radius of a circle given its circumference, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the formula for the circumference of a circle**:
The formula for 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 circumference into the formula**:
We know the circumference \( C \) is 57.2 cm. We can set up the equation:
\[ 57.2 = 2\pi r \]

3. **Use the value of \( \pi \)**:
For calculations, we can use \( \pi \) as \( \frac{22}{7} \). Thus, substituting this value into the equation gives:
\[ 57.2 = 2 \times \frac{22}{7} \times r \]

4. **Simplify the equation**:
First, calculate \( 2 \times \frac{22}{7} \):
\[ 2 \times \frac{22}{7} = \frac{44}{7} \]
Now, substitute this back into the equation:
\[ 57.2 = \frac{44}{7} r \]

5. **Multiply both sides by 7 to eliminate the fraction**:
\[ 57.2 \times 7 = 44r \]
Calculate \( 57.2 \times 7 \):
\[ 57.2 \times 7 = 400.4 \]
So we have:
\[ 400.4 = 44r \]

6. **Divide both sides by 44 to solve for \( r \)**:
\[ r = \frac{400.4}{44} \]
Now, perform the division:
\[ r = 9.1 \text{ cm} \]

7. **Conclusion**:
The radius of the circle is \( 9.1 \) cm.