The circumference of two concentric circle are 176 m and 132 m. What is the difference between their radii?

Options

A. 8 m
B. 9 m
C. 11 m
D. 7 m

Answer

To find the difference between the radii of two concentric circles given their circumferences, we can follow these steps:

### Step 1: Write down 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 2: Set up the equations for the given circumferences
Let \( R_1 \) be the radius of the first circle and \( R_2 \) be the radius of the second circle. According to the problem, we have:
\[ C_1 = 2 \pi R_1 = 176 \, \text{m} \]
\[ C_2 = 2 \pi R_2 = 132 \, \text{m} \]

### Step 3: Solve for the radii
From the circumference equations, we can express the radii in terms of the circumferences:
\[ R_1 = \frac{C_1}{2 \pi} = \frac{176}{2 \pi} \]
\[ R_2 = \frac{C_2}{2 \pi} = \frac{132}{2 \pi} \]

### Step 4: Calculate the difference between the radii
Now, we need to find the difference \( R_1 - R_2 \):
\[ R_1 - R_2 = \frac{176}{2 \pi} - \frac{132}{2 \pi} \]
This simplifies to:
\[ R_1 - R_2 = \frac{176 - 132}{2 \pi} = \frac{44}{2 \pi} = \frac{22}{\pi} \]

### Step 5: Approximate the value of \( \frac{22}{\pi} \)
Using \( \pi \approx 3.14 \):
\[ R_1 - R_2 \approx \frac{22}{3.14} \approx 7 \]

### Conclusion
Thus, the difference between the radii \( R_1 \) and \( R_2 \) is approximately \( 7 \, \text{m} \).