Calculate number of turns for an electric heater

[MisterP]

Homework Statement

Need to calculate, how many turns of nichrome wire do I need on a cylinder to make a heater with resistance of 40 Ω.
Wire diameter = 1mm
Cylinder radius = 2.5cm
R = 40 Ω
Wire diameter = 1mm
Correct answer - 200 turns

Homework Equations

R = ρ*l/S
R = resistance
ρ = specific resistance (I guess) and it is 1.1 Ω⋅mm²/m
l = length of wire
S = area of wire "cross section"

The Attempt at a Solution

Area of wire = Π*r² = 3.14 * 0.5² = 0.785mm²
So I used this formula, but get nowhere close to 200 turns. 40 = 1,1l/0,785...

 

[haruspex]

40 = 1,1l/0,785...

Solving that will give you a length. What is it in turns?

 

[MisterP]

Solving that will give you a length. What is it in turns?

Yes, I know, but it does not add up to near "200" or 0,2 or something like that..
To calculate turns I did this: 3.14 * 5cm (2*r) = 15.7cm is for one turn.
So, 200 turns would be 3140cm.. where did I go wrong?

If I continue with "40 = 1,1l/0,785..." I get 28.57.. let`s just change it to 2857cm.. too short for answer..

 

[haruspex]

Yes, I know, but it does not add up to near "200" or 0,2 or something like that..
To calculate turns I did this: 3.14 * 5cm (2*r) = 15.7cm is for one turn.
So, 200 turns would be 3140cm.. where did I go wrong?

If I continue with "40 = 1,1l/0,785..." I get 28.57.. let`s just change it to 2857cm.. too short for answer..

The difference is about 10%, right?
Note that if you solve it algebraically first the πs cancel and you end up with 200/1.1. So to get 200, you have to take ρ as 1mm²/m.
Looking it up, I see it quoted as 1.1 to 1.5.