There are many points on the circumference of a circle such that distance between each consecutive point is 11cm and time taken to move from one point to next is 45 minute find the radius of circle and no. of points.

Answer

To solve the problem, we need to find the radius of the circle and the number of points on its circumference given that the distance between each consecutive point is 11 cm and the time taken to move from one point to the next is 45 minutes.

### Step 1: Understand the relationship between the circumference, radius, and number of points
The circumference \( C \) of a circle is given by the formula:
\[ C = 2\pi r \]
where \( r \) is the radius of the circle.

If there are \( n \) points on the circumference, and the distance between each consecutive point is 11 cm, then the total distance around the circle (the circumference) can also be expressed as:
\[ C = n \times 11 \]

### Step 2: Set the two expressions for circumference equal to each other
From the two expressions for circumference, we can set them equal:
\[ 2\pi r = n \times 11 \]

### Step 3: Solve for \( n \) in terms of \( r \)
Rearranging the equation gives:
\[ n = \frac{2\pi r}{11} \]

### Step 4: Substitute the value of \( \pi \)
Using \( \pi \approx \frac{22}{7} \), we substitute this value into the equation:
\[ n = \frac{2 \times \frac{22}{7} \times r}{11} \]

### Step 5: Simplify the equation
This simplifies to:
\[ n = \frac{44r}{77} \]
\[ n = \frac{4r}{7} \]

### Step 6: Determine the relationship between \( n \) and \( r \)
From the equation \( n = \frac{4r}{7} \), we can express \( r \) in terms of \( n \):
\[ r = \frac{7n}{4} \]

### Step 7: Find integer values for \( n \)
Since \( n \) must be a whole number (you can't have a fraction of a point), \( n \) must be a multiple of 4. The smallest value for \( n \) that satisfies this is 4.

### Step 8: Calculate the radius using \( n = 4 \)
Substituting \( n = 4 \) back into the equation for \( r \):
\[ r = \frac{7 \times 4}{4} = 7 \text{ cm} \]

### Conclusion
Thus, the radius of the circle is 7 cm and the number of points on the circumference is 4.

### Summary of the Solution
- **Radius of the circle**: 7 cm
- **Number of points**: 4