A lorry travels at 50 km/h. Given that the diameter of its wheel is 88 cm,find how many revolutions per minute the wheel is turning. GIve your answer to the nearest whole number.
At 50 km/h it travels
5000000/60 cm/min
= 250000/3 cm/min
one rotation is 2π(44) or 88π cm
number of rotations per min
= 250000/3 ÷ 88π
or appr 301 rotations per minute
To find the number of revolutions per minute the wheel is turning, we need to first calculate the circumference of the wheel.
The formula for the circumference of a circle is:
Circumference = 2 * π * Radius
Given that the diameter of the wheel is 88 cm, we can find the radius by dividing the diameter by 2:
Radius = Diameter / 2 = 88 cm / 2 = 44 cm
Now, we can calculate the circumference of the wheel:
Circumference = 2 * π * Radius = 2 * π * 44 cm
Next, we convert the circumference from centimeters to kilometers since the speed of the lorry is given in km/h:
Circumference (km) = Circumference (cm) / 100,000
Now, we can find the number of revolutions per minute:
Revolutions per minute = Speed (km/h) / Circumference (km)
Given that the lorry travels at 50 km/h, we substitute the values into the formula:
Revolutions per minute = 50 km/h / (2 * π * 44 cm / 100,000)
Calculating this:
Revolutions per minute ≈ 50 km/h / (2 * 3.14 * 44 cm / 100,000)
Revolutions per minute ≈ 50 / (6.28 * 44 / 100,000)
Revolutions per minute ≈ 50 / (275.2 / 100,000)
Revolutions per minute ≈ 50 / (0.002752)
Revolutions per minute ≈ 18,127
Therefore, the wheel is turning approximately 18,127 revolutions per minute.
To find the number of revolutions per minute the wheel is turning, we need to determine the distance the wheel travels in one minute and then divide it by the circumference of the wheel.
First, let's convert the speed of the lorry from kilometers per hour to centimeters per minute, as the diameter of the wheel is given in centimeters. We know that 1 kilometer is equal to 100,000 centimeters and 1 hour is equal to 60 minutes:
50 km/h = (50 * 100,000) cm / (1 * 60) min = 83,333.33 cm/min (rounded to two decimal places)
Next, we need to calculate the distance the wheel travels in one minute. Since the diameter is given, we can find the circumference of the wheel using the formula: Circumference = π * Diameter.
Circumference = π * 88 cm ≈ 276.46 cm (rounded to two decimal places)
Now, we divide the distance the wheel travels in one minute by the circumference of the wheel:
Revolutions per minute = Distance traveled / Circumference = 83,333.33 cm / 276.46 cm ≈ 301.7 revolutions per minute (rounded to one decimal place)
Finally, we round the result to the nearest whole number as specified in the question:
301.7 ≈ 302 revolutions per minute
Therefore, the wheel is turning approximately 302 revolutions per minute.