Two gates are fitted at the entrance of a library. To open the gates e

1.	Two gates are fitted at the entrance of a library. To open the gates easily, a wheel is fixed at 6 feet distance from the wall into which the gate is fixed. If one of the gates is opened to 90°, find the distance moved by the wheel (π = 3.14).
Answer» Let A be the position of the wall AC be the gate in initial position and AB be position when it is moved 90°. Now the arc length BC gives the distance moved by the wheel. Length of the arc = θ°/360° × 2πr units = 90°/360° × 2 × 3.14 × 6 feets = 3.14 × 3 feets = 9.42 feets ∴ Distance moved by the wheel = 9.42 feets.

Two gates are fitted at the entrance of a library. To open the gates easily, a wheel is fixed at 6 feet distance from the wall into which the gate is fixed. If one of the gates is opened to 90°, find the distance moved by the wheel (π = 3.14).

Answer»

Let A be the position of the wall AC be the gate in initial position and AB be position when it is moved 90°.

Now the arc length BC gives the distance moved by the wheel.

Length of the arc

= θ°/360° × 2πr units

= 90°/360° × 2 × 3.14 × 6 feets

= 3.14 × 3 feets

= 9.42 feets

∴ Distance moved by the wheel = 9.42 feets.