A running track is in the form of a-circle whose inner circumference is 396m and outer circumference is 528m. Find the width-of the track.

Options

A. `21m`
B. `24m`
C. `22m`
D. `33m`

Answer

To solve the problem of finding the width of the running track, we can follow these steps:

### Step 1: Understand the Problem
We have a running track that is in the shape of a circle, with given inner and outer circumferences. We need to find the width of the track, which is the difference between the outer radius and the inner radius.

### Step 2: Define Variables
Let:
- \( r \) = radius of the inner circle
- \( R \) = radius of the outer circle

The width of the track can be expressed as:
\[ \text{Width} = R - r \]

### Step 3: Use the Inner Circumference
The inner circumference of the circle is given as 396 meters. The formula for the circumference of a circle is:
\[ C = 2\pi r \]

Setting the inner circumference equal to 396 meters:
\[ 2\pi r = 396 \]

### Step 4: Solve for the Inner Radius \( r \)
Substituting \( \pi \) with \( \frac{22}{7} \):
\[ 2 \times \frac{22}{7} \times r = 396 \]

Now, simplify the equation:
\[ \frac{44}{7} r = 396 \]

To isolate \( r \), multiply both sides by \( \frac{7}{44} \):
\[ r = 396 \times \frac{7}{44} \]

Calculating this gives:
\[ r = 63 \text{ meters} \]

### Step 5: Use the Outer Circumference
The outer circumference of the circle is given as 528 meters. Using the same circumference formula:
\[ 2\pi R = 528 \]

### Step 6: Solve for the Outer Radius \( R \)
Again substituting \( \pi \) with \( \frac{22}{7} \):
\[ 2 \times \frac{22}{7} \times R = 528 \]

Simplifying:
\[ \frac{44}{7} R = 528 \]

To isolate \( R \), multiply both sides by \( \frac{7}{44} \):
\[ R = 528 \times \frac{7}{44} \]

Calculating this gives:
\[ R = 84 \text{ meters} \]

### Step 7: Calculate the Width of the Track
Now that we have both radii, we can find the width of the track:
\[ \text{Width} = R - r = 84 - 63 = 21 \text{ meters} \]

### Final Answer
The width of the track is **21 meters**.

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