A circular track is such that its inner circumference is 264 m. If the width of the track is 7m, find the cost of track at the rate of Rs 40 per m.

Answer

To solve the problem step-by-step, we will follow these calculations:

### Step 1: Find the inner radius of the circular track.
We know that the inner circumference of the circular track is given by the formula:
\[ C = 2 \pi r \]
Where \( C \) is the circumference and \( r \) is the radius.

Given that the inner circumference is 264 m, we can set up the equation:
\[ 2 \pi r = 264 \]

### Step 2: Solve for the inner radius \( r \).
To find \( r \), we rearrange the equation:
\[ r = \frac{264}{2 \pi} \]

Using \( \pi \approx \frac{22}{7} \):
\[ r = \frac{264}{2 \times \frac{22}{7}} \]
\[ r = \frac{264 \times 7}{2 \times 22} \]
\[ r = \frac{1848}{44} \]
\[ r = 42 \text{ m} \]

### Step 3: Calculate the outer radius of the track.
The width of the track is given as 7 m. Therefore, the outer radius \( R \) is:
\[ R = r + \text{width} \]
\[ R = 42 \text{ m} + 7 \text{ m} = 49 \text{ m} \]

### Step 4: Find the outer circumference of the circular track.
Using the outer radius, we can find the outer circumference:
\[ C_{outer} = 2 \pi R \]
\[ C_{outer} = 2 \pi \times 49 \]
Using \( \pi \approx \frac{22}{7} \):
\[ C_{outer} = 2 \times \frac{22}{7} \times 49 \]
\[ C_{outer} = \frac{44 \times 49}{7} \]
\[ C_{outer} = \frac{2156}{7} = 308 \text{ m} \]

### Step 5: Calculate the cost of the track.
The cost of the track is given at the rate of Rs 40 per meter. Therefore, the total cost is:
\[ \text{Cost} = \text{Circumference} \times \text{Rate} \]
\[ \text{Cost} = 308 \text{ m} \times 40 \text{ Rs/m} \]
\[ \text{Cost} = 12320 \text{ Rs} \]

### Final Answer:
The cost of the track is Rs 12,320.

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