Justin races his bicycle for 90M . A wheel of his bicycle turns 45 times as the bicycle travels this distance. What is the diameter of the wheel?
each rotation covers 90/45 m or 2 m
circumf = πd
πd = 2
d = 2/π m
To find the diameter of the wheel, we need to use the relationship between the circumference of a circle and its diameter. The formula to calculate the circumference of a circle is:
Circumference = 2 * π * radius
However, we are not given the radius of the wheel, but we are given the distance Justin races, which is 90 meters, and the number of times the wheel turns, which is 45.
The distance traveled by Justin is equal to the circumference of the wheel multiplied by the number of revolutions it makes:
Distance = Circumference * Number of revolutions
Since we know the distance and the number of revolutions, we can rearrange the formula to solve for the circumference:
Circumference = Distance / Number of revolutions
Plugging in the values:
Circumference = 90 m / 45 revolutions
Circumference = 2 m
Now we know the circumference of the wheel is 2 meters.
To find the diameter, we can rearrange the formula for circumference to solve for the diameter:
Circumference = 2 * π * radius
Since the circumference is equal to 2 meters, we have:
2 = 2 * π * radius
Dividing both sides of the equation by 2π:
1 = radius
So, the radius of the wheel is 1 meter.
Finally, the diameter is twice the radius:
Diameter = 2 * radius
Diameter = 2 * 1 meter
Diameter = 2 meters
Therefore, the diameter of Justin's bicycle wheel is 2 meters.