A park is in the form of a rectangle `120 mx100 mdot` At the centre of the park there is a circular lawn. The area of park excluding lawn is `8700 m^2` . Find the radius of the circular lawn. `(U s epi(22)/7)`

Options

A. `c^(2)`
B. `(c^(2))/(2)`
C. `(c^(2))/(4)`
D. none of these

Explanation

To find the radius of the circular lawn in the park, we can follow these steps:

### Step 1: Calculate the Area of the Park
The park is in the form of a rectangle with dimensions 120 m and 100 m. The area \( A \) of a rectangle is given by the formula:
\[ A = \text{length} \times \text{breadth} \]
Substituting the given values:
\[ A = 120 \, \text{m} \times 100 \, \text{m} = 12000 \, \text{m}^2 \]

### Step 2: Calculate the Area of the Circular Lawn
We know that the area of the park excluding the lawn is 8700 m². Therefore, the area of the circular lawn can be calculated by subtracting the area excluding the lawn from the total area of the park:
\[ \text{Area of Circular Lawn} = \text{Total Area of Park} - \text{Area Excluding Lawn} \]
\[ \text{Area of Circular Lawn} = 12000 \, \text{m}^2 - 8700 \, \text{m}^2 = 3300 \, \text{m}^2 \]

### Step 3: Use the Area of the Circle Formula
The area \( A \) of a circle is given by the formula:
\[ A = \pi r^2 \]
Where \( r \) is the radius of the circle. We can rearrange this formula to solve for \( r^2 \):
\[ r^2 = \frac{A}{\pi} \]
Substituting the area of the circular lawn and using \( \pi = \frac{22}{7} \):
\[ r^2 = \frac{3300}{\frac{22}{7}} = 3300 \times \frac{7}{22} \]

### Step 4: Simplify the Expression
Calculating the right side:
\[ r^2 = \frac{3300 \times 7}{22} \]
\[ r^2 = \frac{23100}{22} \]
\[ r^2 = 1050 \]

### Step 5: Calculate the Radius
Now, we take the square root of \( r^2 \) to find \( r \):
\[ r = \sqrt{1050} \]
Calculating the square root:
\[ r \approx 32.4 \, \text{m} \]

### Final Answer
The radius of the circular lawn is approximately \( 32.4 \, \text{m} \).

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