A rubber band is use to tie 9 oranges of diameter 8mm.if the band just touches 8 oranges .find the lenght of the band??

clearly the band forms an octagon (with rounded corners) with a diameter of 3 oranges, or 24mm.

Now play around a bit with the dimensions of an octagon.

What formula do i use steve the question look difficult for me that is why i asked help me plz

well, let's assume the octagon is just a regular polygon. It consists of eight isosceles triangles, each with

two sides of 12, and a vertex angle of θ=45°.

So, if the base of each triangle (one side of the octagon) is s,

(s/2) = 12 sin(θ/2)

Now just plug in your numbers and the perimeter is 8s.

If you want to really make things hard, you have to figure the portions of the oranges that form circular arcs at the corners, and the length of the tangent lines forming the straight part of the sides. No thanks.

Thanks steve

To find the length of the rubber band, we need to calculate the total circumference of all the oranges it touches.

Given:
Number of oranges = 9
Diameter of each orange = 8 mm

First, let's determine the circumference of a single orange using the formula:
Circumference = π × Diameter

Since the diameter is 8 mm, the circumference of each orange is:
C = π × 8 mm = 8π mm

Now, we know that the rubber band is just touching 8 out of the 9 oranges. So the total length of the rubber band is equivalent to the sum of the circumferences of those 8 oranges.

Total length of the band = 8 × (8π mm)

To calculate the value, we need to know the approximation of π. Using the value 3.14 for π, we can calculate the final result:

Total length of the band = 8 × (8 × 3.14 mm)
= 201.12 mm

Therefore, the length of the rubber band is approximately 201.12 mm.