The inner circumference of a circular path around a circular lawn is 440 m . What is the radius of the outer circumference of the path , if the path is 14 m wide ?

Options

A. 96 m
B. 84 m
C. 70 m
D. 88 m

Answer

To find the radius of the outer circumference of the circular path, 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: Use the given inner circumference to find the inner radius
We are given that the inner circumference of the circular path is 440 m. We can set up the equation:
\[ 2 \pi r_{\text{inner}} = 440 \]
Substituting \( \pi \) with \( \frac{22}{7} \):
\[ 2 \times \frac{22}{7} \times r_{\text{inner}} = 440 \]

### Step 3: Solve for the inner radius
Now, we can simplify the equation:
\[ \frac{44}{7} r_{\text{inner}} = 440 \]
To isolate \( r_{\text{inner}} \), multiply both sides by \( \frac{7}{44} \):
\[ r_{\text{inner}} = 440 \times \frac{7}{44} \]
Calculating this gives:
\[ r_{\text{inner}} = 10 \times 7 = 70 \text{ m} \]

### Step 4: Calculate the outer radius
The width of the path is given as 14 m. Therefore, the outer radius \( r_{\text{outer}} \) can be calculated by adding the width of the path to the inner radius:
\[ r_{\text{outer}} = r_{\text{inner}} + \text{width} = 70 + 14 = 84 \text{ m} \]

### Final Answer
The radius of the outer circumference of the path is:
\[ \boxed{84 \text{ m}} \]