a wheel of a bicycle has a diameter of 70cm and is rotating at the rate of 200 revolutions per minute calculate the speed of the bicycle in km/hour
diameter of wheel = 70π cm
distance covered in 1 minute = 200(70π)= 14000π cm/min
= 14000π(60/100000) km/h , (100,000 cm in 1 km and 60 min in 1 hour)
= 26.4 km/h
To calculate the speed of the bicycle, we need to first calculate the distance covered by each revolution of the wheel.
The distance covered by each revolution of the wheel is equal to the circumference of the wheel, which can be calculated using the formula:
Circumference = π * diameter
Given that the diameter of the wheel is 70 cm, we can calculate the circumference as follows:
Circumference = π * 70 cm
Circumference ≈ 22/7 * 70 cm
Circumference ≈ 220 cm
Next, we need to calculate the distance covered by the bicycle in one minute, which is equal to the distance covered by one revolution of the wheel multiplied by the number of revolutions per minute:
Distance covered in 1 minute = Circumference * Number of revolutions per minute
Distance covered in 1 minute = 220 cm * 200 revolutions per minute
Distance covered in 1 minute = 44000 cm
To convert the distance from cm to km, we divide it by 100,000:
Distance covered in 1 minute = 44000 cm / 100000
Distance covered in 1 minute ≈ 0.44 km
Finally, to calculate the speed of the bicycle in km/hour, we multiply the distance covered in 1 minute by 60 to get the distance covered in 1 hour:
Distance covered in 1 hour = Distance covered in 1 minute * 60
Distance covered in 1 hour ≈ 0.44 km * 60
Distance covered in 1 hour ≈ 26.4 km/hour
Therefore, the speed of the bicycle is approximately 26.4 km/hour.
To calculate the speed of the bicycle, we first need to find the distance covered by the bicycle in one revolution.
The circumference of a circle can be calculated using the formula C = 2πr, where C is the circumference and r is the radius of the circle.
Given that the diameter of the wheel is 70cm, the radius will be half of the diameter, so r = 35cm.
Therefore, the circumference of the wheel is C = 2π(35cm) = 70π cm.
Since the wheel rotates 200 times per minute, the distance covered by the bicycle in one minute (after 200 revolutions) can be calculated as:
Distance covered in one minute = 200 x 70π cm.
To convert the distance from cm to km, we divide by 100,000 (since there are 100,000 centimeters in a kilometer) and to convert from minutes to hours, we multiply by 60 (since there are 60 minutes in an hour).
Therefore, the speed of the bicycle in km/hour can be calculated as:
Speed = (200 x 70π cm / 100000) x 60.
Now we just need to substitute the value of π into the formula and calculate the result.
Let's assume the value of π is 3.14:
Speed = (200 x 70 x 3.14 cm / 100000) x 60.
Simplifying the calculation:
Speed = (4400 x 3.14 cm / 100000) x 60 = (13816 cm / 100000) x 60 = 0.13816 x 60 km/h.
Therefore, the speed of the bicycle is approximately 8.29 km/hour.