If the difference between the circumference and the radius of a circle is 37 cm, then using `pi=22/7`, what would be the radius of the circle (in cm)?

Options

A. 3.5 cm
B. 7 cm
C. 14 cm
D. 21 cm

Answer

To solve the problem step by step, we will follow the mathematical reasoning based on the information provided.

### Step 1: Understand the given information
We know that the difference between the circumference of a circle and its radius is 37 cm.

### Step 2: Write down 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.

### Step 3: Set up the equation
According to the problem, we have:
\[ C - r = 37 \]
Substituting the formula for circumference into this equation gives:
\[ 2 \pi r - r = 37 \]

### Step 4: Factor out \( r \)
We can factor out \( r \) from the left side:
\[ r(2 \pi - 1) = 37 \]

### Step 5: Substitute the value of \( \pi \)
We are given that \( \pi = \frac{22}{7} \). Substituting this value into the equation gives:
\[ r\left(2 \cdot \frac{22}{7} - 1\right) = 37 \]

### Step 6: Simplify the expression
Calculate \( 2 \cdot \frac{22}{7} \):
\[ 2 \cdot \frac{22}{7} = \frac{44}{7} \]
Now substitute this back into the equation:
\[ r\left(\frac{44}{7} - 1\right) = 37 \]
To subtract 1, convert 1 into a fraction with a denominator of 7:
\[ 1 = \frac{7}{7} \]
So,
\[ \frac{44}{7} - \frac{7}{7} = \frac{44 - 7}{7} = \frac{37}{7} \]
Now the equation becomes:
\[ r\left(\frac{37}{7}\right) = 37 \]

### Step 7: Solve for \( r \)
To isolate \( r \), multiply both sides by the reciprocal of \( \frac{37}{7} \):
\[ r = 37 \cdot \frac{7}{37} \]
The \( 37 \) cancels out:
\[ r = 7 \]

### Conclusion
The radius of the circle is:
\[ \boxed{7 \text{ cm}} \]