A racetrack is in the form of a ring whose inner circumference is 528 m and the outer circumference is 616 m. Find the width of the track.

Answer

To find the width of the racetrack, we will follow these steps:

### Step 1: Understand the Problem
We have a racetrack in the form of a ring with given inner and outer circumferences. We need to find the width of the track.

### Step 2: Write Down the Given Information
- Inner circumference (C_inner) = 528 m
- Outer circumference (C_outer) = 616 m

### Step 3: Use the Formula for Circumference
The formula for the circumference of a circle is given by:
\[ C = 2\pi r \]
where \( r \) is the radius of the circle.

### Step 4: Find the Radius of the Outer Circle
Using the outer circumference:
\[ C_outer = 2\pi R \]
Substituting the values:
\[ 616 = 2 \times \frac{22}{7} \times R \]

### Step 5: Solve for R (Radius of the Outer Circle)
Rearranging the equation:
\[ R = \frac{616 \times 7}{2 \times 22} \]
Calculating:
\[ R = \frac{616 \times 7}{44} \]
\[ R = \frac{4312}{44} \]
\[ R = 98 \text{ m} \]

### Step 6: Find the Radius of the Inner Circle
Using the inner circumference:
\[ C_inner = 2\pi r \]
Substituting the values:
\[ 528 = 2 \times \frac{22}{7} \times r \]

### Step 7: Solve for r (Radius of the Inner Circle)
Rearranging the equation:
\[ r = \frac{528 \times 7}{2 \times 22} \]
Calculating:
\[ r = \frac{528 \times 7}{44} \]
\[ r = \frac{3696}{44} \]
\[ r = 84 \text{ m} \]

### Step 8: Calculate the Width of the Track
The width of the track is the difference between the outer radius and the inner radius:
\[ \text{Width} = R - r \]
Substituting the values:
\[ \text{Width} = 98 - 84 \]
\[ \text{Width} = 14 \text{ m} \]

### Final Answer
The width of the racetrack is **14 meters**.

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