The circumference of a circle is 110 cm. Find its radius (in cm).

Options

A. 35
B. 19.5
C. 17.5
D. 39

Answer

To find the radius of a circle when the circumference is given, 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 that the circumference is 110 cm. Therefore, we can set up the equation:
\[ 2 \pi r = 110 \]

### Step 3: Solve for the radius \( r \).
To isolate \( r \), we first divide both sides of the equation by \( 2 \pi \):
\[ r = \frac{110}{2 \pi} \]

### Step 4: Substitute the value of \( \pi \).
Using \( \pi \approx \frac{22}{7} \), we can substitute this value into the equation:
\[ r = \frac{110}{2 \times \frac{22}{7}} \]

### Step 5: Simplify the equation.
Calculating the denominator:
\[ 2 \times \frac{22}{7} = \frac{44}{7} \]
Thus, the equation becomes:
\[ r = \frac{110 \times 7}{44} \]

### Step 6: Perform the multiplication and division.
Calculating the numerator:
\[ 110 \times 7 = 770 \]
Now divide by 44:
\[ r = \frac{770}{44} \]

### Step 7: Simplify the fraction.
To simplify \( \frac{770}{44} \), we can divide both the numerator and the denominator by 11:
\[ r = \frac{770 \div 11}{44 \div 11} = \frac{70}{4} \]
Now divide both by 2:
\[ r = \frac{35}{2} = 17.5 \]

### Conclusion:
The radius of the circle is \( 17.5 \) cm.

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