A circular ground of radius 7 m is surrounded by a path of width 3.5 m. Find the area of the path `(pi=(22)/(7))`

Options

A. 202 sq.m
B. 154 sq.m
C. 192.5sq.m
D. 346 .5 sq. m

Answer

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

### Step 1: Determine the radius of the circular ground and the outer radius
The radius of the circular ground is given as 7 m. The width of the path surrounding the circular ground is 3.5 m. Therefore, the outer radius (radius of the larger circle that includes the path) can be calculated as:

\[ \text{Outer Radius} = \text{Radius of Circular Ground} + \text{Width of Path} \]
\[ \text{Outer Radius} = 7 \, \text{m} + 3.5 \, \text{m} = 10.5 \, \text{m} \]

### Step 2: Calculate the area of the larger circle (including the path)
The area \(A\) of a circle is given by the formula:

\[ A = \pi r^2 \]

Using the outer radius:

\[ A_{\text{outer}} = \pi (10.5)^2 \]

Substituting \(\pi = \frac{22}{7}\):

\[ A_{\text{outer}} = \frac{22}{7} \times (10.5)^2 \]
\[ A_{\text{outer}} = \frac{22}{7} \times 110.25 \]
\[ A_{\text{outer}} = \frac{22 \times 110.25}{7} = \frac{2425.5}{7} = 346.5 \, \text{m}^2 \]

### Step 3: Calculate the area of the circular ground
Now, we calculate the area of the circular ground:

\[ A_{\text{inner}} = \pi (7)^2 \]
\[ A_{\text{inner}} = \frac{22}{7} \times 49 \]
\[ A_{\text{inner}} = \frac{1078}{7} = 154 \, \text{m}^2 \]

### Step 4: Calculate the area of the path
The area of the path is the difference between the area of the larger circle and the area of the circular ground:

\[ A_{\text{path}} = A_{\text{outer}} - A_{\text{inner}} \]
\[ A_{\text{path}} = 346.5 \, \text{m}^2 - 154 \, \text{m}^2 = 192.5 \, \text{m}^2 \]

### Conclusion
The area of the path surrounding the circular ground is \(192.5 \, \text{m}^2\).