8.9

The volume V of liquid in a spherical tank of radius r is related to the depth h of the liquid by

V = pi * h .^2 *(3*r - h) ./3

Determine h given r = 1 m and V= .5m^3.
Matlab code:

h = -30:30;

r = 1;

V = .5; % m .^3

f = @(h) (pi .* h .^2 .*(3*r - h) ./ 3) - V;

hold on

plot(h , f(h))

h = .43;

delta = .0001;

%Modified secant method

for i = 1:40

    h_new = h - (delta * h * f(h)) ./ (f(h + delta*h) - f(h));

    h = h_new;

    

    plot(h,h, 'r*')

end

hold off

This produces 

The modified secant method was used to pinpoint the solution at .4311