A horse racecourse is in the form of an annular ring whose outer and inner circumferences are 748 m and 396 m. respectively. The width (in m) of the racecourse is: (Take `pi = (22)/7`)

Options

A. 176
B. 88
C. 56
D. 28

Answer

To find the width of the horse racecourse, which is in the form of an annular ring, we need to determine the radii of the outer and inner circles using their circumferences.

### Step-by-Step Solution:

1. **Identify the formulas and given data:**
- The formula for the circumference of a circle is given by:
\[ C = 2 \pi r \]
- Given outer circumference \(C_{outer} = 748 \, m\) and inner circumference \(C_{inner} = 396 \, m\).
- We will take \(\pi = \frac{22}{7}\).

2. **Calculate the outer radius \(R\):**
- Using the outer circumference:
\[ C_{outer} = 2 \pi R \]
Substituting the values:
\[ 748 = 2 \times \frac{22}{7} \times R \]
- Rearranging to find \(R\):
\[ R = \frac{748 \times 7}{2 \times 22} \]
- Simplifying:
\[ R = \frac{748 \times 7}{44} = \frac{5236}{44} = 119 \, m \]

3. **Calculate the inner radius \(r\):**
- Using the inner circumference:
\[ C_{inner} = 2 \pi r \]
Substituting the values:
\[ 396 = 2 \times \frac{22}{7} \times r \]
- Rearranging to find \(r\):
\[ r = \frac{396 \times 7}{2 \times 22} \]
- Simplifying:
\[ r = \frac{396 \times 7}{44} = \frac{2772}{44} = 63 \, m \]

4. **Calculate the width of the racecourse:**
- The width of the racecourse is the difference between the outer radius and inner radius:
\[ \text{Width} = R - r = 119 - 63 = 56 \, m \]

### Final Answer:
The width of the racecourse is \(56 \, m\).

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