If the wheel of a bicycle makes 560 revolutions in travelling 1.1 km what is its radius?

Options

A. 31.25cm
B. 37.75cm
C. 35.15cm
D. 11.25cm

Answer

To find the radius of the bicycle wheel, we can follow these steps:

### Step 1: Understand the relationship between distance, revolutions, and circumference.
The distance traveled by the wheel in one complete revolution is equal to the circumference of the wheel. The formula for the circumference \( C \) of a circle is given by:
\[ C = 2\pi r \]
where \( r \) is the radius of the circle.

### Step 2: Calculate the total distance traveled.
The total distance traveled by the bicycle is given as 1.1 km. We need to convert this distance into meters for consistency:
\[ 1.1 \text{ km} = 1100 \text{ m} \]

### Step 3: Relate the total distance to the number of revolutions.
If the wheel makes 560 revolutions, the total distance \( D \) covered can be expressed as:
\[ D = \text{Number of Revolutions} \times \text{Circumference} \]
Substituting the values we have:
\[ 1100 = 560 \times (2\pi r) \]

### Step 4: Rearrange the equation to solve for the radius \( r \).
We can rearrange the equation to isolate \( r \):
\[ 2\pi r = \frac{1100}{560} \]
\[ r = \frac{1100}{560 \times 2\pi} \]

### Step 5: Simplify the expression.
Calculating \( \frac{1100}{560} \):
\[ \frac{1100}{560} = \frac{11}{5.6} = \frac{110}{56} = \frac{55}{28} \]
Now substituting this back into the equation for \( r \):
\[ r = \frac{55}{28 \times 2\pi} \]

### Step 6: Calculate the value of \( r \).
Using \( \pi \approx \frac{22}{7} \):
\[ r = \frac{55}{28 \times 2 \times \frac{22}{7}} = \frac{55 \times 7}{28 \times 44} \]
Calculating the denominator:
\[ 28 \times 44 = 1232 \]
Thus,
\[ r = \frac{385}{1232} \]
Calculating this gives:
\[ r \approx 0.03125 \text{ m} = 31.25 \text{ cm} \]

### Conclusion:
The radius of the bicycle wheel is approximately \( 31.25 \text{ cm} \).