A bicycle wheel makes 5000 revolutions in moving 11 km. Then the radius of the wheel (in cm) is (Take `pi = (22)/(7)`)

Options

A. 70
B. 35
C. 17.5
D. 140

Answer

To find the radius of the bicycle wheel, we will use the relationship between the distance traveled, the number of revolutions, and the circumference of the wheel.

### Step-by-Step Solution:

1. **Understand the relationship**: The distance traveled by the wheel is equal to the number of revolutions multiplied by 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 wheel.

2. **Set up the equation**: Given that the wheel makes 5000 revolutions to cover a distance of 11 km, we can express this as:
\[ \text{Distance} = \text{Number of Revolutions} \times \text{Circumference} \]
Therefore:
\[ 11 \text{ km} = 5000 \times C \]

3. **Convert distance to meters**: Since 1 km = 1000 meters, we convert 11 km to meters:
\[ 11 \text{ km} = 11 \times 1000 = 11000 \text{ m} \]

4. **Substituting the circumference**: Now we can substitute the circumference into the equation:
\[ 11000 = 5000 \times (2 \pi r) \]

5. **Substituting the value of \(\pi\)**: We are given that \(\pi = \frac{22}{7}\). Thus, we can rewrite the equation:
\[ 11000 = 5000 \times \left(2 \times \frac{22}{7} \times r\right) \]

6. **Simplifying the equation**:
\[ 11000 = 5000 \times \left(\frac{44}{7} r\right) \]
Dividing both sides by 5000:
\[ \frac{11000}{5000} = \frac{44}{7} r \]
Simplifying \(\frac{11000}{5000}\):
\[ \frac{11}{5} = \frac{44}{7} r \]

7. **Cross-multiplying to solve for r**:
\[ 11 \times 7 = 5 \times 44 r \]
\[ 77 = 220 r \]
Dividing both sides by 220:
\[ r = \frac{77}{220} \]

8. **Simplifying the radius**:
\[ r = \frac{7}{20} \text{ meters} \]

9. **Converting radius to centimeters**: Since 1 meter = 100 centimeters, we convert the radius:
\[ r = \frac{7}{20} \times 100 = \frac{700}{20} = 35 \text{ cm} \]

Thus, the radius of the bicycle wheel is **35 cm**.