Circuits - Power and Resistivity

[NemaxameN]

Homework Statement

A 530 W heating coil designed to operate from 110 V is made of Nichrome wire 0.500 mm in diameter.
(a) Assuming that the resistivity of the Nichrome remains constant at its 20.0°C value, find the length of wire used.
(b) If the diameter of the wire were doubled, how long would the wire be if it had the same resistance?

My chart says rhoNichrome=1.1E-6

Homework Equations

P=VI
V=IR
rho=R(A/l)
A=pi*r^2

The Attempt at a Solution

0.5/2=0.25 (radius)
pi*(0.25)^2=0.196mm^2 = A

V=IR => I=V/R
P=V(V/R) => 530=110^2/R
R=22.83 ohms

1.1E-6=22.83(0.196E-6/l)
l=~4.07m

But this answer is wrong. If someone could help me find my mistake in part A, I can work part B. Thanks!

 

[Delphi51]

Looks okay to me. Wikipedia has rhoNichrome= 1.5 E-6 ohm-meter

 

[NemaxameN]

That gave me 2.98m and 11.95m. Both were still wrong. Hmmm. It's possible my teacher made a miscalculation, she does that fairly frequently. Thank you though!