A water tank consists of a cylindrical part of radius r and height h and a hemis

Question

A water tank consists of a cylindrical part of radius r and height h and a hemispherical top. The tank is to be constructed to hold 600 m3 when

lled. The surface area of the cylindrical part is 2 rh, and its volume is r2h. The surface area of the hemispherical top is given by 2 r2, and its volume is given by 2 r3/3. The cost to construct the cylindrical part of the tank is $400 per square meter of surface area; the hemispherical part costs $600 per square meter. Use the fminbnd function to compute the radius that results in the least cost. Compute the corresponding height h.

Explanation / Answer

We have two equation

1. For volume
600 = (r^2)*h + 2*(r^3)/3;
so, h = (600/(r^2) - (2*r)/3);

2. For surface Area
S = 400*2*r*h + 600*2*(r^2)
putting value of h, We have
S = 800*r*(600/(r^2) - 2*r/3);

Matlab

function S = channel(r)
S = 800*r*(600/(r^2) - 2*r/3);
end

r_1 = fminbnd(@channel,0,600);
h_1 = (600/(r_1^2) - (2*r_1)/3);

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