The inner circumference of a 7 m wide circular race track, is 220 m. Find the radius of the outer circle.

Answer

To solve the problem, we need to find the radius of the outer circle of a circular race track given the inner circumference and the width of the track. Here's a step-by-step solution:

### Step 1: Understand the given information
We know that:
- The width of the circular race track is 7 meters.
- The inner circumference of the track is 220 meters.

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

### Step 3: Set up the equation for the inner circle
Given that the inner circumference is 220 meters, we can set up the equation:
\[ 2\pi r_{\text{inner}} = 220 \]
where \( r_{\text{inner}} \) is the radius of the inner circle.

### Step 4: Solve for the inner radius
We can rearrange the equation to solve for \( r_{\text{inner}} \):
\[ r_{\text{inner}} = \frac{220}{2\pi} \]
Using \( \pi \approx \frac{22}{7} \), we can substitute:
\[ r_{\text{inner}} = \frac{220}{2 \times \frac{22}{7}} = \frac{220 \times 7}{44} = \frac{1540}{44} = 35 \text{ meters} \]

### Step 5: Calculate the radius of the outer circle
The radius of the outer circle \( r_{\text{outer}} \) is the inner radius plus the width of the track:
\[ r_{\text{outer}} = r_{\text{inner}} + \text{width} = 35 + 7 = 42 \text{ meters} \]

### Final Answer
The radius of the outer circle is **42 meters**.

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