SOLUTION: The figure shows three circular pipes, all with 12-inch diameters, that are strapped together by a metal band. How long is the band?

Question 1163518: The figure shows three circular pipes, all with 12-inch diameters, that are strapped together by a metal band. How long is the band?
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52788)   (Show Source): You can put this solution on YOUR website!
.

            HINT

the metal band has 3 linear parts of the length 12 inches each;

and 3 arc parts (parts of a circle) of the radius 6 inches.

These 3 parts together have the length equal to the circumference of the circle of the radius of 6 inches.

Having this hint / instructions, complete the assignment on your own.

Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!

There are three sections of the band that are touching the pipes and three sections that are not.

The sections of the band that are touching the pipes each touch the pipe for one-third of the circumference. So the total length of the three sections of the band that are touching the pipes is equal to the circumference of one of the pipes.

Length of band touching the pipes: pi times the diameter = 12pi.

The sections of the band that are not touching the pipes each have a length equal to the combined radii of two of the pipes -- that is, equal to the diameter of each pipe.

Length of band not touching the pipes: 3(12) = 36.

Total length of band: 36+12pi

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