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

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 900 m^3 of fluid when filled. The surface area of the cylindrical part is 2 pi r h, and its volume is pi r^2 h. The surface area of the hemispherical top is given by 2pi r^2, and its volume is given by 2 pi r^3/3. The cost to construct the cylindrical part of the tank is $500 per square meter of surface area, and the hemispherical part costs $1100 per square meter of surface area. a. Plot the cost versus r for 2 lessthanorequalto r lessthanorequalto 10 m with an appropriate title and labeling of axes. b. Use the MIN function to find the least cost and the corresponding r and h. Use a step size of 0.01 m for r. c. Use the FMINBND function to find the least cost and the corresponding r and h. d. Use the FMINSEARCH function to find the least cost and the corresponding r and h. e. Compare your answers from parts b, c, and d and check your results with the plot from part a.

Explanation / Answer

Solution :

The function files are :

function h = height(V,r)

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

function cost = tower(r) h = height(900,r);

cost = 1000*pi*r.*h+1400*pi*r.^2;

>>optimum_r = fminbnd(‘tower’,0,100)

optimum_r =

4.9237

OR

>> optimum_r = fminsearch('tower',0,100)

ans =

4.9238

>>min_cost = tower(optimum_r)

min_cost =

9.1394e+4

>>optimum_h = height(900,optimum_r)

optimum_h = 3.2825

OR

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