a car travels 1 km in which each wheel makes 450 revolutions. Find the radius of its wheel
one rotation covers 2πr metres
so distance covered in 450 rotations
= 450(2πr) = 900πr metres
but 900πr = 1000
r = 1000/(900π) = 10/(9π) m or appr. .3536 m
the radius is 35.36 cm
NO. OF REVOLUTIONS = 450
DISTANCE= 1KM = 1000M
CIRCUMFERENCE = 1000 450 = O.22 M
0.22= (2)(227)R
1.54= 44R
1.54/4= R
0.353535 M = R
R= 35.35 cm
To find the radius of the wheel, we can use the formula:
Circumference of the wheel = 2πr
Given that each wheel makes 450 revolutions to travel 1 km, we can determine the distance traveled by one wheel in one revolution as follows:
Distance traveled by one wheel in one revolution = 1 km / 450
Now, let's calculate the circumference of the wheel using the formula:
Circumference of the wheel = Total distance traveled by one wheel / Number of revolutions made
Substituting the values we found earlier:
2πr = (1 km / 450) / 450
Now, to find the radius (r), we can solve for it by rearranging the formula:
r = ((1 km / 450) / 450) / (2π)
Let's calculate the value of r using this formula.
To find the radius of the car's wheel, we need to use the information about the distance traveled and the number of wheel revolutions.
The circumference of a circle is given by the formula C = 2πr, where C is the circumference and r is the radius.
We know that the distance traveled by the car is 1 kilometer, which is equal to 1000 meters. We also know that each wheel makes 450 revolutions.
Since each revolution corresponds to the circumference of the wheel, we can find the total distance traveled by the car in terms of the wheel's circumference.
Total distance traveled = Number of wheel revolutions × Circumference of the wheel
In this case, the total distance traveled is 1000 meters, and the number of wheel revolutions is 450.
So, 1000 meters = 450 × Circumference of the wheel
Now, we need to rearrange the equation to solve for the circumference of the wheel.
Circumference of the wheel = 1000 meters / 450
Now we can substitute the value of the circumference into the formula C = 2πr to find the radius.
2πr = Circumference of the wheel
Let's calculate the radius:
r = (Circumference of the wheel) / (2π)
Substituting the value of the circumference, we get:
r = (1000 meters / 450) / (2π)
r ≈ 0.706 meters
Therefore, the radius of the wheel is approximately 0.706 meters.