A steering wheel is rotated through 128°, Its radius is 22 cm. How far would a point on the steering wheel’s edge move? *
s = rθ = 22*(128/180)*π = ____ cm
To find how far a point on the steering wheel's edge would move, we need to calculate the arc length of the circular path traced by that point.
The formula for arc length is given by:
Arc Length = (Central Angle / 360°) * Circumference
To calculate the central angle, we are given that the steering wheel is rotated through 128°.
Next, we need to calculate the circumference of the steering wheel's edge. The circumference of a circle is given by the formula:
Circumference = 2 * π * radius
Substituting the given radius of 22 cm into the formula, we get:
Circumference = 2 * 3.14 * 22 cm
Now, we can plug in these values into the arc length formula:
Arc Length = (128° / 360°) * (2 * 3.14 * 22 cm)
Simplifying this calculation, we get:
Arc Length = (0.3556) * (138.16 cm)
Finally, calculating the result:
Arc Length ≈ 49.07 cm
Therefore, a point on the steering wheel's edge would move approximately 49.07 cm.