% Parameters
V = 0.35;       % [m^3]
L = 3;          % [m]
r = 0.3;        % [m]

% Initial guess
h = 0;          % [m]

% Loop until convergence
hold = 1;
iter = 0; % Counter to limit # of iterations, in case of no convergence
while abs(h - hold) > 1e-7 && iter < 100
    % Compute the value of the function
    f = L*(r^2*acos(h/r) - h*sqrt(r^2-h^2)) - V;

    % Compute the derivative of the function
    fderiv = -2*L*sqrt(r^2-h^2);

    % Compute the Newton update
    hold = h;  % Remember old value for comparison
    h = h - f / fderiv;

    % Increase the counter for the number of iterations
    iter = iter + 1;
end;

% Display result with an accuracy of 6 digits
fprintf('h = %.6fn', h);  % h = 0.041306