Measurement of a circle question

Question

Suppose the blades of a wind turbine are 16' long. What is the distance traveled by a point on its tip as the blade rotates 3/5 of a revolution?

(must use π key and round to the nearest tenth

Answer 1

Arc length of a circle is S = rθ for measurement in radians.

3/5 of a revolution is θ=2π(3/5) =1.2π.

S = 16(1.2π) = 19.2π ft.

Answer 2

Assumptions: Wind Turbine Rotor and Hub are considered the center point.

Step 1 Provide your given information as variables

Wind Turbines have blades that create a circular object. Each blade length represents the radius of the circle created.

Blade Length = Radius (R) = 16 feet

A point at the tip of the blade follows the circumference of the circle.

The point at the tip travels 3/5 revolutions of the circle which needs to be converted to radians (π).

1 rev = 2π

3/5 rev = 6π/5

Rotation = θ = 6π/5

Step 2 Find the arc length

We use the arc length of a circle to find part of the circumference of a circle.

The formula for arc length is S = Rθ.

S = (16 ft) x (6π/5)

The point traveled 16 x (6π/5) feet.