The circumference of a circular garden is 66 m . Find its diameter.(Take `pi=(22)/(7))`

Options

A. 25 m
B. 24 m
C. 21 m
D. 27 m

Answer

To find the diameter of a circular garden when the circumference is given, we can follow these steps:

### Step-by-Step Solution:

1. **Understand 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.

2. **Substitute the given circumference**:
We know the circumference \( C \) is 66 meters. Therefore, we can write:
\[ 2 \pi r = 66 \]

3. **Use the value of \( \pi \)**:
We are given \( \pi = \frac{22}{7} \). Substitute this value into the equation:
\[ 2 \times \frac{22}{7} \times r = 66 \]

4. **Simplify the equation**:
Multiply \( 2 \) and \( \frac{22}{7} \):
\[ \frac{44}{7} r = 66 \]

5. **Isolate \( r \)**:
To find \( r \), multiply both sides of the equation by \( \frac{7}{44} \):
\[ r = 66 \times \frac{7}{44} \]

6. **Calculate \( r \)**:
Simplify the right-hand side:
\[ r = \frac{66 \times 7}{44} \]
First, simplify \( \frac{66}{44} \):
\[ \frac{66}{44} = \frac{3}{2} \quad \text{(since 66 and 44 can both be divided by 22)} \]
Now substitute back:
\[ r = \frac{3}{2} \times 7 = \frac{21}{2} = 10.5 \text{ meters} \]

7. **Find the diameter**:
The diameter \( d \) of the circle is given by:
\[ d = 2r \]
Substitute the value of \( r \):
\[ d = 2 \times 10.5 = 21 \text{ meters} \]

### Final Answer:
The diameter of the circular garden is **21 meters**.