The inner circumference of a circular race track 7 m wide is 440 m. Find the radius of the outer circle.

Options

A. 57 m
B. 68 m
C. 77 m
D. 69 m

Answer

To find the radius of the outer circle of a circular race track that is 7 meters wide and has an inner circumference of 440 meters, we can follow these steps:

### Step 1: Understand the relationship between circumference and radius
The circumference \( C \) of a circle is given by the formula:
\[ C = 2\pi r \]
where \( r \) is the radius of the circle.

### Step 2: Calculate the radius of the inner circle
Given that the inner circumference is 440 meters, we can set up the equation:
\[ 2\pi r_{\text{inner}} = 440 \]
To find \( r_{\text{inner}} \), we rearrange the equation:
\[ r_{\text{inner}} = \frac{440}{2\pi} \]

### Step 3: Substitute the value of \( \pi \)
Using \( \pi \approx 3.14 \):
\[ r_{\text{inner}} = \frac{440}{2 \times 3.14} = \frac{440}{6.28} \approx 70.06 \text{ meters} \]

### Step 4: Calculate the radius of the outer circle
Since the width of the track is 7 meters, the radius of the outer circle \( r_{\text{outer}} \) can be calculated as:
\[ r_{\text{outer}} = r_{\text{inner}} + 7 \]
Substituting the value of \( r_{\text{inner}} \):
\[ r_{\text{outer}} = 70.06 + 7 = 77.06 \text{ meters} \]

### Step 5: Round the answer
For practical purposes, we can round the radius of the outer circle to:
\[ r_{\text{outer}} \approx 77 \text{ meters} \]

### Final Answer
The radius of the outer circle is approximately **77 meters**.

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