A bicycle wheel of radius 35cm is making 25 revolutions in 10secs. At what speed in km/hr is the cyclle moving
I rotation = 70π cm
25(70π) cm per 10 sec
6(25)(70π) cm per minute
60(6)(25)(70π)/100 m per hour
6300π m/hr
6300π/1000 km/h
= appr 19.8 km/h
First, let's calculate the distance travelled by the bicycle wheel in one revolution.
The circumference of a circle is given by the formula: C = 2πr, where r is the radius.
First, let's convert the radius from centimeters to meters:
Radius = 35 cm = 35/100 = 0.35 meters
The circumference of the wheel is:
C = 2π(0.35) ≈ 2.2 meters
Next, let's calculate the distance travelled in 25 revolutions:
Distance = 25 × C ≈ 25 × 2.2 meters
Now, let's calculate the time taken to travel this distance:
Time = 10 seconds
Finally, let's calculate the speed in km/hr:
Step 1: Convert meters to kilometers:
Distance in kilometers = (25 × 2.2)/1000
Step 2: Convert seconds to hours:
Time in hours = 10/3600
Step 3: Calculate the speed:
Speed = Distance in kilometers / Time in hours
Speed = ((25 × 2.2)/1000) / (10/3600)
Speed = ((25 × 2.2) × 3600) / (1000 × 10)
Simplifying further,
Speed = (25 × 2.2 × 3600)/(10000)
Speed = 198 km/hr (rounded to the nearest kilometer per hour)
Therefore, the speed of the bicycle is approximately 198 km/hr.
To find the speed of the bicycle in km/hr, we need to determine the distance covered by the bicycle in 10 seconds and then convert it to kilometers per hour.
First, we need to find the distance covered in 10 seconds by the circumference of the wheel.
The circumference of a circle can be calculated using the formula: Circumference = 2 * π * radius.
Given that the radius of the bicycle wheel is 35 cm, we can substitute this value into the formula:
Circumference = 2 * π * 35 cm.
Next, we calculate the distance covered in 10 seconds by multiplying the circumference of the wheel by the number of revolutions made in that time:
Distance covered in 10 seconds = Circumference * Number of revolutions.
The number of revolutions in 10 seconds is given as 25, so we substitute this value into the formula:
Distance covered in 10 seconds = Circumference * 25.
Finally, we convert the distance covered in 10 seconds to kilometers and hours. We know that 1 kilometer is equal to 1000 meters and 1 hour is equal to 3600 seconds.
To convert the distance from centimeters to kilometers, we divide by 100,000 (since there are 100,000 centimeters in a kilometer).
To convert the time from seconds to hours, we divide by 3600.
Now, let's calculate the speed in km/hr:
Circumference = 2 * π * 35 cm ≈ 220 cm.
Distance covered in 10 seconds ≈ 220 cm * 25 = 5500 cm.
Distance covered in 10 seconds in kilometers ≈ 5500 cm / 100,000 = 0.055 km.
Time in hours ≈ 10 sec / 3600 = 0.00278 hours.
Speed in km/hr = (Distance covered in 10 seconds in kilometers / Time in hours)
≈ 0.055 km / 0.00278 hours ≈ 19.78 km/hr.
Therefore, the speed of the bicycle is approximately 19.78 km/hr.