The circumference of a circle is 66 cm. Find its radius (in cm).

Options

A. 21
B. 10.5
C. 4.5
D. 9

Answer

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

### Step 1: Write down 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.

### Step 2: Substitute the given circumference into the formula.
We know from the problem that the circumference \( C \) is 66 cm. Therefore, we can write:
\[ 66 = 2 \pi r \]

### Step 3: Use the approximate value of \( \pi \).
For calculations, we can use \( \pi \approx \frac{22}{7} \). Substituting this value into the equation gives:
\[ 66 = 2 \times \frac{22}{7} \times r \]

### Step 4: Simplify the equation.
Now, simplify the right side:
\[ 66 = \frac{44}{7} r \]

### Step 5: Solve for \( r \).
To isolate \( r \), multiply both sides by \( 7 \):
\[ 66 \times 7 = 44r \]
\[ 462 = 44r \]

Now, divide both sides by 44:
\[ r = \frac{462}{44} \]

### Step 6: Simplify the fraction.
Now, simplify \( \frac{462}{44} \):
\[ r = \frac{231}{22} \]

### Step 7: Calculate the value of \( r \).
Now, perform the division:
\[ r = 10.5 \text{ cm} \]

### Conclusion:
The radius of the circle is \( 10.5 \) cm.