tree pipes of diameter 1 m are held together by a taut metal band as shown. Find the length in meters, of the metal band.

Join the centres and you will have an equilateral triangle with sides 1 m

Also the band will form 3 arcs , each of 120°.
So the band covers the entire distance around the circle, that is, its circumference.
Notice that if you complete the rectangle, we know the long side is 1 m

total distance = 2π(.5) + 3(1)
= (π+ 3) m

WRONG:)

To calculate the length of the metal band, we need to determine the circumference of the circle formed by the arrangement of the pipes.

The circumference of a circle is given by the formula C = 2πr, where C is the circumference and r is the radius of the circle.

Since the diameter of each pipe is 1 meter, the radius of each pipe is half of the diameter, which is 1/2 meter or 0.5 meters.

Since there are three pipes held together, the arrangement forms a circle with a radius of 0.5 meters.

Now, we can calculate the circumference of the circle:
C = 2πr
C = 2π(0.5)
C = π meters

So, the length of the metal band is π meters or approximately 3.14 meters.

To find the length of the metal band, we first need to calculate the circumference of each pipe and then add them together.

The circumference of a circle can be found using the formula:
Circumference = π * diameter

Given that the diameter of each pipe is 1 meter, we can calculate the circumference of one pipe as follows:
Circumference = π * 1 = π meters

Now, since there are three pipes held together, we multiply the circumference of one pipe by 3:
Total Circumference = 3 * π = 3π meters

Therefore, the length of the metal band is 3π meters.