A wheel has a radius of 6.6 m. How far (path length) does a point on the circumference travel if the wheel is rotated through an angle of 52.0°?

To find the distance traveled by a point on the circumference of a wheel when it is rotated through a given angle, we need to use the formula for the arc length of a circle. The arc length formula is given by:

Arc Length = (Angle / 360) × (2 × π × Radius)

In this case, the radius of the wheel is given as 6.6 m and the angle of rotation is given as 52.0°.

Now, let's substitute the values into the formula and calculate the arc length:

Arc Length = (52.0° / 360) × (2 × π × 6.6 m)

To simplify the calculation, we can convert the angle from degrees to radians. Since 1° is equal to π/180 radians, we have:

Angle (in radians) = Angle (in degrees) × (π / 180)

So, the angle of rotation in radians is:

52.0° × (π / 180) = 0.9076 radians (rounded to four decimal places)

Substituting this value into the arc length formula, we get:

Arc Length = (0.9076) × (2 × π × 6.6 m)

Simplifying further:

Arc Length = 0.9076 × 2 × 3.1416 × 6.6 m

Arc Length = 35.1205 m (rounded to four decimal places)

Therefore, a point on the circumference of the wheel travels a path length of approximately 35.1205 meters when the wheel is rotated through an angle of 52.0°.