Certainly! Let's break this down into detailed steps to find the total distance covered by a bicycle wheel with a diameter of 42 cm after 300 complete revolutions.
### Step 1: Understand the Given Values
- Diameter of the wheel: 42 cm
- Number of revolutions: 300
- Approximation for π (pi): [tex]\(\frac{22}{7}\)[/tex]
### Step 2: Calculate the Circumference of the Wheel
The circumference [tex]\( C \)[/tex] of a circle can be calculated using the formula:
[tex]\[ C = \pi \times d \][/tex]
where [tex]\( d \)[/tex] is the diameter.
Given:
[tex]\[ d = 42 \, \text{cm} \][/tex]
[tex]\[ \pi = \frac{22}{7} \][/tex]
So,
[tex]\[ C = \frac{22}{7} \times 42 \][/tex]
### Step 3: Simplify the Calculation for Circumference
First, we can simplify the multiplication:
[tex]\[
C = \frac{22}{7} \times 42 = 22 \times 6 = 132 \, \text{cm}
\][/tex]
### Step 4: Calculate the Total Distance Covered in Centimeters
The total distance [tex]\( D \)[/tex] covered can be found by multiplying the circumference of the wheel by the number of revolutions:
[tex]\[ D = C \times \text{Number of Revolutions} \][/tex]
[tex]\[ D = 132 \, \text{cm} \times 300 \][/tex]
### Step 5: Perform the Multiplication
[tex]\[ D = 132 \times 300 = 39600 \, \text{cm} \][/tex]
### Step 6: Convert the Distance from Centimeters to Meters
Since there are 100 centimeters in a meter, we can convert the distance:
[tex]\[ D = \frac{39600 \, \text{cm}}{100} \][/tex]
[tex]\[ D = 396 \, \text{m} \][/tex]
### Final Answer
The total distance covered by the bicycle wheel in meters after 300 complete revolutions is:
[tex]\[ 396 \, \text{meters} \][/tex]
So, the step-by-step solution leads us to the conclusion that the total distance covered by the bicycle wheel is 396 meters.
