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

Total_Volume = 600;

r = linspace(2, 10, 1000);

h = (600 - ((2*pi*r.^3)/3))./(pi * (r.^2));

Total_Cost = (400*2*pi.*r.*h) + (600*2*pi*r.^2);

%Now we will determine minumum cost and correspondence radius

[Min_Cost, Index] = min(Total_Cost)

Min_r = r(Index)

Corresponding_h = h(Index)

plot(r,Total_Cost)

xlabel ('Radius (Meter)')

ylabel ('Cost ($)')

title ('Cost versus Radius')

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.