A car travels 0.99 km in which each wheel makes 450 complete revolutions. Find radius of the wheel.

Answer

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

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

### Step 2: Calculate the total distance traveled in meters
The car travels a distance of 0.99 km. To convert this distance into meters:
\[ 0.99 \text{ km} = 0.99 \times 1000 \text{ m} = 990 \text{ m} \]

### Step 3: Relate the total distance to the number of revolutions
The total distance traveled by the car can also be expressed in terms of the number of revolutions and the circumference of the wheel:
\[ \text{Total Distance} = \text{Number of Revolutions} \times \text{Circumference} \]
Given that the car makes 450 revolutions, we can write:
\[ 990 \text{ m} = 450 \times C \]
Substituting the expression for circumference:
\[ 990 = 450 \times (2\pi r) \]

### Step 4: Solve for the radius \( r \)
Rearranging the equation to solve for \( r \):
\[ 990 = 450 \times 2\pi r \]
\[ r = \frac{990}{450 \times 2\pi} \]

### Step 5: Substitute the value of \( \pi \)
Using \( \pi \approx \frac{22}{7} \):
\[ r = \frac{990}{450 \times 2 \times \frac{22}{7}} \]
\[ r = \frac{990 \times 7}{450 \times 2 \times 22} \]

### Step 6: Simplify the expression
Calculating the denominator:
\[ 450 \times 2 \times 22 = 19800 \]
Now substituting back:
\[ r = \frac{6930}{19800} \]

### Step 7: Final calculation
Now we divide:
\[ r = 0.35 \text{ m} \]

### Conclusion
The radius of the wheel is \( 0.35 \) meters.

---