Question

A 3​-ft wide circular track for a camera dolly is set up for a movie scene. The two rails of the track form concentric circles. The radius of the inner circle is 53 ft. How much farther does a wheel on the outer rail travel than a wheel on the inner rail of the track in one​ turn? Two circles are concentric. The smaller circle has radius 53 feet. The distance between the two circles is 3 feet. 53 ft 3 ft The wheel on the outer rail travels nothing feet farther than the wheel on the inner rail of the track in one turn.

Answer 1

Answer:

Outer wheel will cover 18.84 ft more than the inner wheel.

Step-by-step explanation:

We can draw a figure in which two rails are formed by two concentric circles with a distance 3 ft between them.

Outer circle has the radius = (53 + 3) = 56 ft

Radius of the inner circle = 53 ft

In one turn wheel of the outer circle will cover more distance  than the wheel on the inner rail.

So difference in the distance covered by both the wheels = Circumference of outer circle - circumference of inner circle

= 2π(R - r) where R = radius of the outer circle

                            r = radius of the inner circle

Therefore, extra distance covered by the outer wheel = 2π(56 - 53)

= 6π

= 6×(3.14)

= 18.84 ft