SOLUTION: Three curtain rods, each with diameter 6 cm, are bound together by a band, as illustrated. Find the length of the band, in cm.
Diagram: https://imgur.com/a/s4QHMXr
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Diagram: https://imgur.com/a/s4QHMXr
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Question 1148933: Three curtain rods, each with diameter 6 cm, are bound together by a band, as illustrated. Find the length of the band, in cm.
Diagram: https://imgur.com/a/s4QHMXr Found 2 solutions by Boreal, ikleyn:Answer by Boreal(15235) (Show Source):
You can put this solution on YOUR website! the radius is 3 cm.
The two radii where the band is tangent to a circle, are at an angle of 120 degrees.
There are 2*3=6 radii where the band is not touching a circle
There are 3*120 degrees or one full circle where the band reaches a circle
the radii are 3 cm, so that distance is 18 cm
The other distance is 6 pi, the circumference of one circle
The total distance is 18+6 pi or 36.85 cm or 37 cm.
The length of the band is three times the length of the 120 degrees arc of the circle of the radius of 3 cm
PLUS 3 times the distance between the centers of the rods.
In other words,
The length of the band = + 3*(2*3) = + 3*6 = 2*3.14*3 + 3*6 = 36.84 cm (approximately). ANSWER
