The wheel of an engine turns 350 times round its axle to cover a distance of 1.76 km. The diameter of the wheel is

Options

A. 3 cm
B. 3a`//3 cm`
C. 9 cm
D. V3 cm

Answer

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

### Step 1: Understand the relationship between distance, revolutions, and circumference.
The wheel covers a distance of 1.76 km after 350 revolutions. The distance covered in one revolution is equal to the circumference of the wheel.

### Step 2: Convert kilometers to meters.
Since 1 km = 1000 meters, we convert 1.76 km to meters:
\[ 1.76 \text{ km} = 1.76 \times 1000 = 1760 \text{ meters} \]

### Step 3: Calculate the distance covered in one revolution.
To find the distance covered in one revolution, we divide the total distance by the number of revolutions:
\[ \text{Distance per revolution} = \frac{1760 \text{ meters}}{350} = \frac{1760}{350} \text{ meters} \]

### Step 4: Simplify the fraction.
We can simplify \(\frac{1760}{350}\):
\[ \frac{1760 \div 10}{350 \div 10} = \frac{176}{35} \text{ meters} \]

### Step 5: Use the circumference formula to find the radius.
The circumference \(C\) of a circle is given by the formula:
\[ C = 2 \pi r \]
Setting the circumference equal to the distance per revolution:
\[ 2 \pi r = \frac{176}{35} \]

### Step 6: Solve for the radius \(r\).
Rearranging the equation to solve for \(r\):
\[ r = \frac{176}{35 \times 2 \pi} \]
Using \(\pi \approx \frac{22}{7}\):
\[ r = \frac{176}{35 \times 2 \times \frac{22}{7}} = \frac{176 \times 7}{35 \times 2 \times 22} \]

### Step 7: Calculate the value of \(r\).
Calculating the denominator:
\[ 35 \times 2 \times 22 = 1540 \]
Thus,
\[ r = \frac{1232}{1540} \]
Simplifying:
\[ r = \frac{88}{110} = \frac{8}{10} = 0.8 \text{ meters} \]

### Step 8: Calculate the diameter \(d\).
The diameter \(d\) is twice the radius:
\[ d = 2r = 2 \times 0.8 = 1.6 \text{ meters} \]

### Step 9: Convert the diameter to centimeters.
Since 1 meter = 100 centimeters:
\[ d = 1.6 \times 100 = 160 \text{ centimeters} \]

### Final Answer:
The diameter of the wheel is **160 centimeters**.

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