A 64 cm wide path is made around a circular garden having a diameter of 10 metres .The area (in `m^(2))` of the path is closed to :
(Take `pi=(22)/(7))`

Options

A. a)211
B. b)115
C. c)94
D. d)100

Answer

To find the area of the path made around a circular garden, we can follow these steps:

### Step 1: Convert the width of the path from centimeters to meters.
The width of the path is given as 64 cm. To convert this to meters:
\[ 64 \text{ cm} = \frac{64}{100} \text{ m} = 0.64 \text{ m} \]

**Hint:** Remember that 1 meter = 100 centimeters.

### Step 2: Calculate the radius of the circular garden.
The diameter of the circular garden is given as 10 meters. The radius \( r \) is half of the diameter:
\[ r = \frac{10}{2} = 5 \text{ m} \]

**Hint:** The radius is always half of the diameter.

### Step 3: Calculate the outer radius of the garden including the path.
The outer radius \( R \) is the radius of the garden plus the width of the path:
\[ R = r + \text{width of the path} = 5 + 0.64 = 5.64 \text{ m} \]

**Hint:** When adding the path's width, ensure both measurements are in the same unit.

### Step 4: Calculate the area of the larger circle (including the path).
The area \( A_{\text{outer}} \) of the larger circle is given by the formula:
\[ A_{\text{outer}} = \pi R^2 \]
Substituting the value of \( R \):
\[ A_{\text{outer}} = \pi (5.64)^2 \]

**Hint:** Use \( \pi \approx \frac{22}{7} \) as given in the question.

### Step 5: Calculate the area of the smaller circle (the garden).
The area \( A_{\text{inner}} \) of the smaller circle is:
\[ A_{\text{inner}} = \pi r^2 \]
Substituting the value of \( r \):
\[ A_{\text{inner}} = \pi (5)^2 \]

### Step 6: Calculate the area of the path.
The area of the path \( A_{\text{path}} \) is the difference between the area of the larger circle and the area of the smaller circle:
\[ A_{\text{path}} = A_{\text{outer}} - A_{\text{inner}} \]
Substituting the areas we calculated:
\[ A_{\text{path}} = \pi (5.64^2 - 5^2) \]

### Step 7: Simplify the expression.
Using the difference of squares:
\[ 5.64^2 - 5^2 = (5.64 + 5)(5.64 - 5) = (10.64)(0.64) \]
Thus, we have:
\[ A_{\text{path}} = \pi \times 10.64 \times 0.64 \]

### Step 8: Substitute \( \pi \) and calculate.
Substituting \( \pi = \frac{22}{7} \):
\[ A_{\text{path}} = \frac{22}{7} \times 10.64 \times 0.64 \]

### Step 9: Perform the multiplication.
Calculating \( 10.64 \times 0.64 \):
\[ 10.64 \times 0.64 = 6.8096 \]
So,
\[ A_{\text{path}} = \frac{22}{7} \times 6.8096 \]

### Step 10: Calculate the final area.
Calculating \( \frac{22 \times 6.8096}{7} \):
\[ A_{\text{path}} \approx \frac{149.792}{7} \approx 21.4 \text{ m}^2 \]

### Conclusion:
The area of the path is approximately \( 21.4 \text{ m}^2 \).

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