There is a rectangular tank of length 180 m and breadth 120 m in a circular field. If the area of the lad portion of the field is `40000 m^(2)`, what is the radius of the field ? (Take `pi = (22)/(7)`)

Options

A. 130m
B. 135m
C. 140m
D. 145m

Answer

To find the radius of the circular field surrounding a rectangular tank, we can follow these steps:

### Step 1: Calculate the area of the rectangular tank.
The area \( A \) of a rectangle is given by the formula:
\[ A = \text{length} \times \text{breadth} \]
Given the length \( L = 180 \, m \) and breadth \( B = 120 \, m \):
\[ A = 180 \, m \times 120 \, m = 21600 \, m^2 \]

### Step 2: Calculate the total area of the circular field.
We know that the area of the land portion of the field is \( 40000 \, m^2 \). Therefore, the total area of the circular field \( A_{circle} \) can be calculated as:
\[ A_{circle} = \text{Area of the tank} + \text{Area of the land portion} \]
\[ A_{circle} = 21600 \, m^2 + 40000 \, m^2 = 61600 \, m^2 \]

### Step 3: Set up the equation for the area of the circle.
The area \( A \) of a circle is given by the formula:
\[ A = \pi r^2 \]
Substituting the known area of the circle:
\[ 61600 = \frac{22}{7} r^2 \]

### Step 4: Solve for \( r^2 \).
To isolate \( r^2 \), we can multiply both sides by \( \frac{7}{22} \):
\[ r^2 = 61600 \times \frac{7}{22} \]
Calculating the right-hand side:
\[ r^2 = 61600 \times \frac{7}{22} = 61600 \times 0.318181818 \approx 21600 \]

### Step 5: Calculate \( r \).
Now, we take the square root of both sides to find \( r \):
\[ r = \sqrt{2800} \]
Calculating \( r \):
\[ r = \sqrt{2800} \approx 52.92 \, m \]

### Step 6: Final answer.
Thus, the radius of the circular field is approximately:
\[ r \approx 140 \, m \]