if the diameter of a bike wheel is 20cm, what's the minimum number of revolutions needed to cover 1km?
1km = 1000 m
100cm = 1 m
convert to meters and divide
Diameter d = 20 cm
Circumference C = pi * d
C = 3.14 * 20 = 62.8 cm in one revolution
62.8 cm
100 cm = 1m
62.8/100 = 0.628 m
0.628 m in one revolution
1 km = 1000 m
1000/0.628 = 1592.36 revolutions
To find the minimum number of revolutions needed to cover 1 km, we need to calculate the distance traveled by the wheel in one revolution and then divide 1 km by that distance.
The distance traveled by the wheel in one revolution is equal to the circumference of the wheel. The formula for the circumference of a circle is C = π * d, where C represents the circumference and d represents the diameter.
Given that the diameter of the bike wheel is 20 cm, we can calculate the circumference as follows:
C = π * d
C = π * 20
C ≈ 62.83 cm
Now, let's convert 1 km into centimeters, as the circumference is in cm:
1 km = 100,000 cm
To find the minimum number of revolutions needed to cover 1 km, we divide the total distance by the distance traveled in one revolution:
Number of revolutions = 100,000 cm / 62.83 cm ≈ 1591.55
Therefore, the minimum number of revolutions needed to cover 1 km is approximately 1592 revolutions.
To determine the minimum number of revolutions needed to cover a certain distance, you need to calculate the distance covered per revolution.
The formula to calculate the distance covered per revolution is:
Distance covered per revolution = Circumference of the wheel
The circumference of a circle is calculated as:
Circumference = 2 * π * Radius
In this case, the radius of the wheel is half of the diameter, so it would be 20 cm / 2 = 10 cm.
Now, let's calculate the circumference:
Circumference = 2 * π * 10 cm
To convert the distance from centimeters to kilometers, we need to divide it by 100,000 because there are 1,000,000 centimeters in a kilometer.
Distance covered per revolution in kilometers = (Circumference in centimeters) / 100,000
Substituting the values:
Distance covered per revolution in kilometers = (2 * π * 10 cm) / 100,000
Now, let's calculate the minimum number of revolutions needed to cover 1 km:
Minimum number of revolutions = Distance to be covered / Distance covered per revolution in kilometers
Substituting the values:
Minimum number of revolutions = 1 km / ((2 * π * 10 cm) / 100,000)
Simplifying the equation:
Minimum number of revolutions = 100,000 / (2 * π * 10 cm)
Finally, to find the answer, you can calculate this expression:
Minimum number of revolutions ≈ 1591.5
Therefore, the minimum number of revolutions needed to cover 1 km is approximately 1591.5 revolutions.