A horse takes `2(1)/(2)` seconds to complete a round around a circular field. If the speed of the horse was 66m/sec, then the radius of the field is,
[Given `pi = (22)/(7)`]

Options

A. 25.62 m
B. 26.52 m
C. 25.26 m
D. 26.25 m

Answer

To find the radius of the circular field that the horse runs around, we can follow these steps:

### Step 1: Understand the relationship between speed, time, and distance
The formula to calculate distance is:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]

### Step 2: Convert the time taken into seconds
The time taken by the horse to complete one round is given as \(2 \frac{1}{2}\) seconds. This can be converted into an improper fraction:
\[ 2 \frac{1}{2} = \frac{5}{2} \text{ seconds} \]

### Step 3: Calculate the distance covered in one round
Using the speed of the horse (66 m/s) and the time taken (\(\frac{5}{2}\) seconds), we can calculate the distance:
\[ \text{Distance} = \text{Speed} \times \text{Time} = 66 \times \frac{5}{2} \]
Calculating this gives:
\[ \text{Distance} = 66 \times 2.5 = 165 \text{ meters} \]

### Step 4: Relate the distance to the circumference of the circular field
The distance covered in one round is equal to the circumference of the circular field, which is given by the formula:
\[ \text{Circumference} = 2 \pi r \]
Setting this equal to the distance we calculated:
\[ 2 \pi r = 165 \]

### Step 5: Substitute the value of \(\pi\)
We are given that \(\pi = \frac{22}{7}\). Substituting this into the equation:
\[ 2 \times \frac{22}{7} \times r = 165 \]
This simplifies to:
\[ \frac{44}{7} r = 165 \]

### Step 6: Solve for \(r\)
To isolate \(r\), multiply both sides by \(\frac{7}{44}\):
\[ r = 165 \times \frac{7}{44} \]
Calculating this gives:
\[ r = \frac{1155}{44} \]
Now, simplifying \(\frac{1155}{44}\):
\[ r = \frac{105}{4} = 26.25 \text{ meters} \]

### Final Answer
The radius of the field is \( \boxed{26.25} \) meters.

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