A thin plastic band 50 cm long is used to tie seven plastic pipes together. What is the radius of the pipe?

The shape is a hexagon but not vertices but curved.

My solution was , you get an eqilateral triangle with side 3 r
3 r = 50/6
r = 50/6/3
= 2.73

But the text book answer is 25/(pi+6)

25 / ( pi + 6 ) =

25 / ( 3.1415926535 + 6 ) =

25 / 9.1415926535 =

2.734753226

approx. = 2.73

What is problem?

How do you get it in terms of pi?

I see pi in Bosnian's calculations.

Where do you get the equilateral triangle with sides 3r from?

To find the radius of the pipe using the given information, we can approach it by considering the shape formed by the plastic band when it is used to tie the seven plastic pipes together.

From the given information, we know that the plastic band is 50 cm long. We also know that the shape formed is a curved hexagon.

One way to solve this is by considering the inner circle of the hexagon formed by the plastic pipes. The circumference of this inner circle will be equal to the length of the plastic band.

To find the circumference of the inner circle, we can divide the length of the plastic band by the number of sides of the hexagon (which is 6). In this case, the circumference will be 50 cm / 6 = 8.33 cm.

The circumference of a circle is given by the formula 2πr, where r is the radius of the circle. Therefore, we have:

2πr = 8.33 cm

To solve for the radius, we can rearrange the equation:

r = 8.33 cm / (2π)
r ≈ 1.33 cm

So, based on this calculation, the radius of the plastic pipe is approximately 1.33 cm.

It's important to note that this calculation assumes that the shape formed by the plastic band is a perfect hexagon. If the shape is slightly distorted or not a regular hexagon, there may be some variation in the calculated radius.