Find the diameter of a circle if its circumference is 66 cm.

Options

A. 41 cm
B. 31 cm
C. 21 cm
D. 51 cm

Answer

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

### Step-by-Step Solution:

1. **Understand the given information**:
- The circumference of the circle is given as 66 cm.

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

3. **Set up the equation**:
- We can set the circumference equal to the given value:
\[ 2\pi r = 66 \]

4. **Substitute the value of \(\pi\)**:
- For calculations, we can use \(\pi \approx \frac{22}{7}\). Thus, we rewrite the equation:
\[ 2 \times \frac{22}{7} \times r = 66 \]

5. **Simplify the equation**:
- Multiply both sides by 7 to eliminate the fraction:
\[ 2 \times 22 \times r = 66 \times 7 \]
\[ 44r = 462 \]

6. **Solve for the radius (r)**:
- Divide both sides by 44:
\[ r = \frac{462}{44} \]
- Simplifying this gives:
\[ r = \frac{231}{22} = 10.5 \text{ cm} \]

7. **Calculate the diameter (d)**:
- The diameter (d) is twice the radius:
\[ d = 2r = 2 \times 10.5 = 21 \text{ cm} \]

8. **Final Answer**:
- The diameter of the circle is 21 cm.