The inner and outer radius of a circular track are 56 m and 63m respectively. Find the area of the track

Answer

To find the area of the circular track, we will follow these steps:

### Step 1: Identify the inner and outer radius
- The inner radius (r) is given as 56 m.
- The outer radius (R) is given as 63 m.

### Step 2: Calculate the area of the outer circle
The formula for the area of a circle is given by:
\[ \text{Area} = \pi R^2 \]
Substituting the outer radius:
\[ \text{Area of outer circle} = \pi (63)^2 \]
Calculating \(63^2\):
\[ 63^2 = 3969 \]
Thus,
\[ \text{Area of outer circle} = \pi \times 3969 \]

### Step 3: Calculate the area of the inner circle
Using the same formula for the inner circle:
\[ \text{Area of inner circle} = \pi (56)^2 \]
Calculating \(56^2\):
\[ 56^2 = 3136 \]
Thus,
\[ \text{Area of inner circle} = \pi \times 3136 \]

### Step 4: Calculate the area of the track
The area of the track is the difference between the area of the outer circle and the area of the inner circle:
\[ \text{Area of track} = \text{Area of outer circle} - \text{Area of inner circle} \]
Substituting the areas we calculated:
\[ \text{Area of track} = \pi \times 3969 - \pi \times 3136 \]
Factoring out \(\pi\):
\[ \text{Area of track} = \pi (3969 - 3136) \]
Calculating the difference:
\[ 3969 - 3136 = 833 \]
Thus,
\[ \text{Area of track} = \pi \times 833 \]

### Step 5: Substitute the value of \(\pi\)
Using \(\pi \approx \frac{22}{7}\):
\[ \text{Area of track} = \frac{22}{7} \times 833 \]

### Step 6: Calculate the final area
Calculating:
\[ \text{Area of track} = \frac{22 \times 833}{7} \]
Calculating \(22 \times 833\):
\[ 22 \times 833 = 18326 \]
Now, divide by 7:
\[ \text{Area of track} = \frac{18326}{7} \approx 2618 \]

### Final Answer
The area of the track is approximately:
\[ \text{Area of track} \approx 2618 \, \text{m}^2 \]

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