Around a circular garden, a 5 m wide path is made, if the radius of the garden be 15m, then find the area of the path.

Options

A. `225 pi` sq.m
B. `400 pi` sq. m
C. `175 pi` sq. m
D. 200 sq. m

Answer

To find the area of the path around the circular garden, we will follow these steps:

### Step 1: Identify the radius of the garden and the path
- The radius of the garden (inner circle) is given as 15 m.
- The width of the path is 5 m. Therefore, the radius of the outer circle (garden + path) will be:
\[ \text{Radius of outer circle} = \text{Radius of garden} + \text{Width of path} = 15 \, \text{m} + 5 \, \text{m} = 20 \, \text{m} \]

### Step 2: Calculate the area of the outer circle
- The area of a circle is calculated using the formula:
\[ \text{Area} = \pi r^2 \]
- For the outer circle (radius = 20 m):
\[ \text{Area of outer circle} = \pi (20)^2 = \pi \times 400 = 400\pi \, \text{m}^2 \]

### Step 3: Calculate the area of the inner circle (garden)
- For the inner circle (radius = 15 m):
\[ \text{Area of inner circle} = \pi (15)^2 = \pi \times 225 = 225\pi \, \text{m}^2 \]

### Step 4: Find the area of the path
- The area of the path is the difference between the area of the outer circle and the area of the inner circle:
\[ \text{Area of path} = \text{Area of outer circle} - \text{Area of inner circle} \]
\[ \text{Area of path} = 400\pi - 225\pi = (400 - 225)\pi = 175\pi \, \text{m}^2 \]

### Step 5: Final answer
- Thus, the area of the path around the circular garden is:
\[ \text{Area of path} = 175\pi \, \text{m}^2 \]