The differences between the circumference and diameter of a circle is 60 cm, then radius is

Options

A. 12 cm
B. 13 cm
C. 14 cm
D. 15 cm

Answer

To solve the problem step by step, we need to find the radius of a circle given that the difference between the circumference and the diameter is 60 cm.

### Step 1: Understand the formulas
The formulas we need are:
- Circumference (C) of a circle: \( C = 2\pi r \)
- Diameter (D) of a circle: \( D = 2r \)

### Step 2: Set up the equation
According to the problem, the difference between the circumference and the diameter is 60 cm. We can express this as:
\[ C - D = 60 \]
Substituting the formulas for circumference and diameter:
\[ 2\pi r - 2r = 60 \]

### Step 3: Factor out common terms
We can factor out \( 2r \) from the left side of the equation:
\[ 2r(\pi - 1) = 60 \]

### Step 4: Solve for \( r \)
Now, we can isolate \( r \) by dividing both sides by \( 2(\pi - 1) \):
\[ r = \frac{60}{2(\pi - 1)} \]
\[ r = \frac{30}{\pi - 1} \]

### Step 5: Substitute the value of \( \pi \)
Using the approximation \( \pi \approx \frac{22}{7} \):
\[ r = \frac{30}{\frac{22}{7} - 1} \]
First, calculate \( \frac{22}{7} - 1 \):
\[ \frac{22}{7} - 1 = \frac{22}{7} - \frac{7}{7} = \frac{15}{7} \]

### Step 6: Substitute back into the equation for \( r \)
Now substitute this back into the equation for \( r \):
\[ r = \frac{30}{\frac{15}{7}} \]
When you divide by a fraction, it is the same as multiplying by its reciprocal:
\[ r = 30 \times \frac{7}{15} \]

### Step 7: Simplify the expression
Now simplify:
\[ r = \frac{30 \times 7}{15} = \frac{210}{15} = 14 \]

### Conclusion
Thus, the radius \( r \) of the circle is:
\[ r = 14 \, \text{cm} \]