If the area of a circular pond is `49pisq.` ft what will be the cost of erecting a 2 feet high wall around it at Rs 50 per feet ?

Answer

To solve the problem step by step, we will follow these steps:

### Step 1: Identify the given information
We know that the area of the circular pond is given as \(49\pi\) square feet.

### Step 2: Use the formula for the area of a circle
The formula for the area of a circle is:
\[ \text{Area} = \pi r^2 \]
Where \(r\) is the radius of the circle.

### Step 3: Set up the equation
We can set up the equation using the given area:
\[ \pi r^2 = 49\pi \]

### Step 4: Simplify the equation
We can divide both sides of the equation by \(\pi\) (since \(\pi\) is not zero):
\[ r^2 = 49 \]

### Step 5: Solve for the radius
Now, we take the square root of both sides:
\[ r = \sqrt{49} = 7 \text{ feet} \]
So, the radius of the circular pond is 7 feet.

### Step 6: Calculate the circumference of the circle
The circumference \(C\) of a circle is given by the formula:
\[ C = 2\pi r \]
Substituting the radius we found:
\[ C = 2\pi(7) = 14\pi \text{ feet} \]
Using \(\pi \approx 3.14\) for calculation:
\[ C \approx 14 \times 3.14 = 43.96 \text{ feet} \approx 44 \text{ feet} (rounded) \]

### Step 7: Calculate the cost of erecting the wall
The height of the wall is 2 feet, but we are interested in the length of the wall for cost calculation. The cost per foot of the wall is Rs 50.

The total cost for the wall is:
\[ \text{Total Cost} = \text{Cost per foot} \times \text{Length of the wall} \]
Substituting the values:
\[ \text{Total Cost} = 50 \times 44 = 2200 \text{ Rs} \]

### Final Answer
The cost of erecting the 2 feet high wall around the pond is Rs 2200.

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