The circumference of a circle exceeds its diameter by 18 cm. Find the radius of the circle.

Answer

To solve the problem step by step, we can follow these instructions:

### Step 1: Understand the relationship between circumference and diameter
The circumference (C) of a circle is given by the formula:
\[ C = 2\pi r \]
where \( r \) is the radius of the circle.

The diameter (D) of a circle is related to the radius by:
\[ D = 2r \]

### Step 2: Set up the equation based on the problem statement
According to the problem, the circumference exceeds the diameter by 18 cm. Therefore, we can write the equation as:
\[ C = D + 18 \]

Substituting the formulas for circumference and diameter into this equation gives:
\[ 2\pi r = 2r + 18 \]

### Step 3: Substitute the value of \( \pi \)
For simplicity, we can use \( \pi \approx \frac{22}{7} \). Thus, we can rewrite the equation:
\[ 2 \cdot \frac{22}{7} r = 2r + 18 \]

### Step 4: Simplify the equation
Now, simplifying the left side:
\[ \frac{44}{7} r = 2r + 18 \]

### Step 5: Eliminate the fraction
To eliminate the fraction, multiply every term by 7:
\[ 44r = 14r + 126 \]

### Step 6: Rearrange the equation
Now, we can rearrange the equation to isolate \( r \):
\[ 44r - 14r = 126 \]
\[ 30r = 126 \]

### Step 7: Solve for \( r \)
Now, divide both sides by 30 to find \( r \):
\[ r = \frac{126}{30} \]

### Step 8: Simplify the fraction
Now simplify \( \frac{126}{30} \):
\[ r = \frac{21}{5} \]
This can also be expressed as:
\[ r = 4.2 \text{ cm} \]

### Final Answer
The radius of the circle is \( 4.2 \text{ cm} \).

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