Find the radius of a circle whose circumference is 176 cm.

Options

A. `38`cm
B. `28`cm
C. `18`cm
D. `25`cm

Answer

To find the radius of a circle whose circumference is 176 cm, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the formula for circumference**:
The circumference \( C \) of a circle is given by the formula:
\[ C = 2\pi r \]
where \( r \) is the radius and \( \pi \) (pi) is approximately \( \frac{22}{7} \).

2. **Set up the equation**:
We know the circumference \( C \) is 176 cm. Therefore, we can set up the equation:
\[ 176 = 2\pi r \]

3. **Substitute the value of \( \pi \)**:
Substitute \( \pi \) with \( \frac{22}{7} \):
\[ 176 = 2 \times \frac{22}{7} \times r \]

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:
\[ 176 = \frac{44}{7} r \]

5. **Isolate \( r \)**:
To find \( r \), multiply both sides by \( \frac{7}{44} \) to isolate \( r \):
\[ r = 176 \times \frac{7}{44} \]

6. **Calculate \( r \)**:
First, simplify \( \frac{176}{44} \):
\[ \frac{176}{44} = 4 \]
Now, multiply by 7:
\[ r = 4 \times 7 = 28 \text{ cm} \]

### Final Answer:
The radius of the circle is \( 28 \text{ cm} \).

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