If the circumference of a circle is 110 cm , find its radius .

Options

A. `19.5` cm.
B. `17.5` cm.
C. `18.5` cm.
D. `15.5` cm.

Answer

To find the radius of a circle when the circumference is given, we can follow these steps:

### Step-by-Step Solution:

1. **Write down the formula for the circumference of a circle.**
The formula for the circumference (C) of a circle is:
\[ C = 2 \pi r \]
where \( r \) is the radius and \( \pi \) is a constant approximately equal to 3.14 (or \( \frac{22}{7} \) for calculations).

2. **Substitute the given circumference into the formula.**
We know that the circumference of the circle is 110 cm. Therefore, we can set up the equation:
\[ 110 = 2 \pi r \]

3. **Rearrange the equation to solve for the radius (r).**
To isolate \( r \), we can divide both sides of the equation by \( 2 \pi \):
\[ r = \frac{110}{2 \pi} \]

4. **Substitute the value of \( \pi \).**
We will use \( \pi = \frac{22}{7} \):
\[ r = \frac{110}{2 \times \frac{22}{7}} \]

5. **Simplify the expression.**
First, calculate \( 2 \times \frac{22}{7} \):
\[ 2 \times \frac{22}{7} = \frac{44}{7} \]
Now substitute this back into the equation for \( r \):
\[ r = \frac{110}{\frac{44}{7}} = 110 \times \frac{7}{44} \]

6. **Perform the multiplication.**
Simplifying \( 110 \times \frac{7}{44} \):
\[ r = \frac{110 \times 7}{44} \]

7. **Simplify the fraction.**
We can simplify \( \frac{110}{44} \) first:
\[ \frac{110}{44} = \frac{55}{22} = \frac{5}{2} \]
Therefore:
\[ r = \frac{5}{2} \times 7 = \frac{35}{2} \]

8. **Convert to decimal form.**
Finally, converting \( \frac{35}{2} \) into decimal gives:
\[ r = 17.5 \text{ cm} \]

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

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