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.
1 answer:
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
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