Find the diameter of a circle whose circumference is 66 cm.

Options

A. `22` cm
B. `21`cm
C. `23` cm
D. `24` cm

Answer

To find the diameter of a circle whose circumference is 66 cm, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the relationship between circumference and diameter**:
The circumference (C) of a circle is related to its diameter (D) by the formula:
\[ C = \pi D \]
where \(\pi\) (Pi) is approximately \(3.14\) or can be represented as \(\frac{22}{7}\).

2. **Substitute the given circumference into the formula**:
We know the circumference is 66 cm, so we can set up the equation:
\[ 66 = \pi D \]
Using \(\pi = \frac{22}{7}\), we can rewrite the equation as:
\[ 66 = \frac{22}{7} D \]

3. **Isolate the diameter (D)**:
To find D, we need to multiply both sides of the equation by \(7\) to eliminate the fraction:
\[ 66 \times 7 = 22 D \]
This simplifies to:
\[ 462 = 22 D \]

4. **Divide both sides by 22**:
Now, we can solve for D by dividing both sides by 22:
\[ D = \frac{462}{22} \]

5. **Calculate the value**:
Performing the division:
\[ D = 21 \]

6. **Conclusion**:
Therefore, the diameter of the circle is:
\[ D = 21 \text{ cm} \]