A radius of a circular park is 23 m. It has inside all around it. a 4 m wide path. Find the cost of paving the path at the rate of Rs. `500//m^2`. (Take `pi = 22/7`)

Options

A. Rs. 2,10,000
B. Rs. 2,64,000
C. Rs. 2,60,000
D. Rs. 2,40,000

Answer

To solve the problem step by step, we need to find the area of the path surrounding the circular park and then calculate the cost of paving that area.

### Step 1: Find the radius of the circular park and the outer radius including the path.
- Given the radius of the circular park (R) = 23 m.
- The width of the path = 4 m.
- Therefore, the outer radius (R_outer) = R + width of the path = 23 m + 4 m = 27 m.

**Hint:** Remember to add the width of the path to the radius of the park to find the outer radius.

### Step 2: Calculate the area of the circular park.
- Area of a circle = π * r².
- Here, we use the inner radius (R) = 23 m.
- Area of the park (A_park) = π * (23)² = (22/7) * 529 = 1658 m².

**Hint:** Use the formula for the area of a circle and substitute the radius correctly.

### Step 3: Calculate the area of the larger circle (including the path).
- Area of the larger circle (A_outer) = π * (R_outer)² = π * (27)² = (22/7) * 729 = 2286 m².

**Hint:** Again, use the area formula and ensure you square the outer radius.

### Step 4: Find the area of the path.
- Area of the path = Area of the outer circle - Area of the inner circle.
- Area of the path = A_outer - A_park = 2286 m² - 1658 m² = 628 m².

**Hint:** Subtract the area of the inner circle from the area of the outer circle to find the area of the path.

### Step 5: Calculate the cost of paving the path.
- Cost of paving per m² = Rs. 500.
- Total cost = Area of the path * Cost per m² = 628 m² * 500 Rs/m² = Rs. 314000.

**Hint:** Multiply the area of the path by the cost per square meter to find the total cost.

### Final Answer:
The total cost of paving the path is Rs. 314000.