A race track is in the form of a ring whose inner and outer circumferences are 44cm and 66 cm respectively. Find the width of the track.

Answer

To find the width of the race track, we will 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: Set up the equations for the inner and outer circumferences
Given the inner circumference is 44 cm, we can set up the equation for the inner radius \( R_1 \):
\[ 2\pi R_1 = 44 \]

Similarly, for the outer circumference which is 66 cm, we set up the equation for the outer radius \( R_2 \):
\[ 2\pi R_2 = 66 \]

### Step 3: Solve for the inner radius \( R_1 \)
Rearranging the equation for the inner circumference:
\[ R_1 = \frac{44}{2\pi} \]
Substituting \( \pi \) with \( \frac{22}{7} \):
\[ R_1 = \frac{44}{2 \times \frac{22}{7}} = \frac{44 \times 7}{44} = 7 \text{ cm} \]

### Step 4: Solve for the outer radius \( R_2 \)
Now, rearranging the equation for the outer circumference:
\[ R_2 = \frac{66}{2\pi} \]
Substituting \( \pi \) with \( \frac{22}{7} \):
\[ R_2 = \frac{66}{2 \times \frac{22}{7}} = \frac{66 \times 7}{44} = 10.5 \text{ cm} \]

### Step 5: Calculate the width of the track
The width of the track is the difference between the outer radius and the inner radius:
\[ \text{Width} = R_2 - R_1 = 10.5 \text{ cm} - 7 \text{ cm} = 3.5 \text{ cm} \]

### Final Answer
The width of the track is **3.5 cm**.

---