help with numerical analysis

if true
fplot('pi*x*sqrt((x)^2+((750/pi)^2)/(x)^4)',[0,10]);
[R fmin]=fminbnd('pi*x*sqrt((x)^2+((750/pi)^2)/(x)^4)',0,8);
h=170/(pi*R^2);
grid on
fprintf('The Value of R is %5.4f cm and the Height is %5.4f cm\n',R,h)
end

a paper cup shaped as a cone is designed to have a volume of 250cm^3. Determine the radius R and height h such that the least amount of paper will be used for making cup my answers came up as

Value of R is 5.5267 cm and the Height is 1.7716 cm but the book says is Value of R is 6.9632cm and the height is 4.9237 any advice or any mistakes that you can point out, thanks

Answer 1

[Andrei Bobrov]

syms R H V real
H = 3*V/(pi*R^2);
S = subs(pi*R*sqrt(  R^2/4+H^2  ),V,250);
Rout = double(solve(diff(S,R),R));
Rout = Rout(Rout>0&imag(Rout)==0)
Hout = double(subs(H,{V,R},{250,Rout}))

OR

[R fmin]=fminbnd(@(x)pi*x.*sqrt(x.^2/4+(750/pi)^2./x.^4),0,8)

[francis]

thanks for your help , I try to type your first part and it gives me this error code, how can I solve that? thanks again ??? Error using ==> sym.subs at 214 Elements of the substitution cell array must be of the same size.

Answer 2

[Raghavendra]

Basically the equation for cone says Volume(V)= (Pi*r*r*h)/3; You have two unknown variable, Lets assume the radius = 2, then you can use this formula to find out the Height.