Error in Newton-Raphson Method

Given:

Why is this code running so long? I'm not getting the expected value, which is just over 5, any help is appreciated.

%% Problem 3b. Newton-Raphson Method (Needs Work)

clear all

clc

R=15/2;

v=500;

h=8;

i=1;

while (1)

fh=(pi^R*h^2-pi/(3*h^3-v));

fph=2*pi*R*h-pi*h^2;

hnew=h-fh/fph;

err=abs((hnew-h)/hnew);

if err<(1*10^(-8))break,end

if hnew<0

h=(hnew+h)/2;

else

h=hnew;

end

i=i+1;

end

i

h

Answer 1

[Alan Stevens]

Like this

R=15/2;
v=500;
h=8;
i=1;
err = 1;
while err>10^-8 && i<100
    hold = h;
    fh = pi*h^2*(3*R - h)/3 - v;
    fph=pi*(2*h*R - h^2);
    h=h-fh/fph;
    err=abs((h-hold)/h);
    i=i+1;
end
disp(h)