If a circular grass lawn of 35 m in radius has a path 7 m wide running around it on the outside, then the area of the path is

Options

A. 1450 `m^(2)`
B. 1576 `m^(2)`
C. 1694 `m^(2)`
D. 3368 `m^(2)`

Answer

To find the area of the path surrounding the circular grass lawn, we can follow these steps:

### Step 1: Identify the radius of the circular lawn and the width of the path.
- The radius of the circular grass lawn (R1) = 35 m
- The width of the path = 7 m

### Step 2: Calculate the radius of the outer circle (which includes the path).
- The radius of the outer circle (R2) = Radius of the lawn + Width of the path
- R2 = 35 m + 7 m = 42 m

### Step 3: Calculate the area of the outer circle (which includes the path).
- The formula for the area of a circle is given by:
\[ \text{Area} = \pi r^2 \]
- Therefore, the area of the outer circle (A_outer) = π × (R2)^2
- A_outer = π × (42 m)^2 = π × 1764 m²

### Step 4: Calculate the area of the inner circle (the lawn).
- The area of the inner circle (A_inner) = π × (R1)^2
- A_inner = π × (35 m)^2 = π × 1225 m²

### Step 5: Calculate the area of the path.
- The area of the path (A_path) = Area of the outer circle - Area of the inner circle
- A_path = A_outer - A_inner
- A_path = (π × 1764 m²) - (π × 1225 m²)
- A_path = π × (1764 m² - 1225 m²)
- A_path = π × 539 m²

### Step 6: Substitute the value of π (using 22/7 for calculation).
- A_path = (22/7) × 539 m²
- A_path = 22 × 539 / 7
- A_path = 11858 / 7
- A_path = 1694 m²

### Conclusion:
The area of the path is **1694 m²**.

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