What will the cost of leveling a circular ground of diameter 28 m, if the charges are Rs 125 per sq. m `(pi=22//7)`

Options

A. A) Rs 76,000
B. B) Rs 76,400
C. C) Rs. 77,800
D. D) Rs 77,000

Answer

To find the cost of leveling a circular ground with a diameter of 28 m at a rate of Rs 125 per square meter, we can follow these steps:

### Step 1: Calculate the radius of the circular ground.
The radius (r) is half of the diameter.
\[ \text{Radius} = \frac{\text{Diameter}}{2} = \frac{28 \, \text{m}}{2} = 14 \, \text{m} \]

### Step 2: Calculate the area of the circular ground.
The area (A) of a circle is given by the formula:
\[ A = \pi r^2 \]
Using \(\pi = \frac{22}{7}\) and substituting the radius:
\[ A = \frac{22}{7} \times (14)^2 \]
Calculating \(14^2\):
\[ 14^2 = 196 \]
Now substituting this value into the area formula:
\[ A = \frac{22}{7} \times 196 \]
We can simplify this:
\[ A = \frac{22 \times 196}{7} \]
Calculating \(196 \div 7 = 28\):
\[ A = 22 \times 28 = 616 \, \text{m}^2 \]

### Step 3: Calculate the cost of leveling the ground.
The cost is calculated by multiplying the area by the cost per square meter:
\[ \text{Cost} = \text{Area} \times \text{Cost per sq. m} = 616 \, \text{m}^2 \times 125 \, \text{Rs/m}^2 \]
Calculating the cost:
\[ \text{Cost} = 616 \times 125 \]
Breaking it down:
\[ 616 \times 125 = 616 \times (100 + 25) = 61600 + 15400 = 77000 \, \text{Rs} \]

### Final Answer:
The cost of leveling the circular ground is Rs 77,000.

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