Thread: shape of tapered bottle.

I wonder if anyone can help me. I need to design a sticker to cover a jar which will be used to collect money for charity. The relevant part of the jar is 405mm in circumference at the top, and 390mm in circumference at a point 85mm lower. How can I plot the shape to use as my outline on my computer, so that when printed and cut-out and stuck on it will be straight all round at the top of the jar?
Hope I've made it all clear.

Hello, bigginge!

We want a sector of an annulus (ring).

Code:

              * * *..
          *     |:::::* 405
        *       |:::::::*
       *        *:: 390 :*
            *   |   *:::::
      *    *    |@   *::::*
      *    *    *----*----*
      *    *-      r * 85 *
            *       *
       *        *        *
        *               *
          *           *
              * * *

The radius of the smaller circle is
The sector has central angle
The arc length on the smaller circle is 390 mm.

The radius of the larger circle is
The arc length on the lartger circle is 405 mm.


Arc length formula: . . with in radians.

Smaller circle: . .[1]

Larger circle: . .[2]

Substitute [1] into [2]: .

And we have: .

Substitute into [1]: .


Construct two concentric circles with radii 2210 mm and 2295 mm.
Cut out a sector with central angle of radians or about 10.1 degrees.

The label is the curved region between the two circles.

Thank you! It's been about 45 years since I got my maths O level and I didn't understand the first part, but I did the summary in Adobe Illustrator and it looks just right.
Thanks again.