The area of a circular garden is 2464 sq.m. How much distance will have to be covered if you like to cross the garden along its diameter ? (Use `pi = (22)/(7)`)

Options

A. 56m
B. 48 m
C. 28 m
D. 24 m

Answer

To solve the problem, we need to find the distance that will be covered when crossing the circular garden along its diameter. We start with the area of the circular garden, which is given as 2464 sq.m.

### Step-by-Step Solution:

1. **Formula for Area of a Circle**:
The area \( A \) of a circle is given by the formula:
\[ A = \pi r^2 \]
where \( r \) is the radius of the circle.

2. **Substituting the Given Area**:
We know the area \( A = 2464 \) sq.m and we will use \( \pi = \frac{22}{7} \). So we can set up the equation:
\[ 2464 = \frac{22}{7} r^2 \]

3. **Solving for \( r^2 \)**:
To isolate \( r^2 \), we multiply both sides by \( \frac{7}{22} \):
\[ r^2 = 2464 \times \frac{7}{22} \]

4. **Calculating \( r^2 \)**:
First, calculate \( 2464 \times 7 \):
\[ 2464 \times 7 = 17248 \]
Now divide by 22:
\[ r^2 = \frac{17248}{22} = 784 \]

5. **Finding the Radius \( r \)**:
Now, we take the square root of \( r^2 \):
\[ r = \sqrt{784} = 28 \text{ m} \]

6. **Calculating the Diameter**:
The diameter \( d \) of the circle is given by:
\[ d = 2r = 2 \times 28 = 56 \text{ m} \]

### Final Answer:
The distance that will have to be covered if you cross the garden along its diameter is **56 meters**.

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