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

Options

A. 154
B. 44
C. 14
D. 7

Answer

To solve the problem step by step, we need to find the radius of the circle given that the difference between the circumference and the radius is 37 cm.

### Step 1: Write the formulas for circumference and the given condition
The circumference \( C \) of a circle is given by the formula:
\[ C = 2 \pi r \]
According to the problem, the difference between the circumference and the radius is 37 cm:
\[ C - r = 37 \]

### Step 2: Substitute the formula for circumference into the equation
Substituting the formula for circumference into the equation gives:
\[ 2 \pi r - r = 37 \]

### Step 3: Factor out the radius \( r \)
We can factor out \( r \) from the left side:
\[ r(2 \pi - 1) = 37 \]

### Step 4: Substitute the value of \( \pi \)
Using \( \pi = \frac{22}{7} \), we substitute this value into the equation:
\[ r\left(2 \times \frac{22}{7} - 1\right) = 37 \]

### Step 5: Simplify the expression
Calculating \( 2 \times \frac{22}{7} \):
\[ 2 \times \frac{22}{7} = \frac{44}{7} \]
Now substitute this back into the equation:
\[ r\left(\frac{44}{7} - 1\right) = 37 \]
To subtract 1, we convert 1 into a fraction with a denominator of 7:
\[ 1 = \frac{7}{7} \]
Thus, we have:
\[ r\left(\frac{44}{7} - \frac{7}{7}\right) = 37 \]
This simplifies to:
\[ r\left(\frac{44 - 7}{7}\right) = 37 \]
\[ r\left(\frac{37}{7}\right) = 37 \]

### Step 6: Solve for \( r \)
To isolate \( r \), multiply both sides by \( \frac{7}{37} \):
\[ r = 37 \times \frac{7}{37} \]
This simplifies to:
\[ r = 7 \text{ cm} \]

### Final Answer
The radius of the circle is \( 7 \) cm.

---