MATLAB Use Matlab to write a script and post the script and the result. A water
ID: 3814523 • Letter: M
Question
MATLAB
Use Matlab to write a script and post the script and the result.
A water tank consists of a cylindrical part of radius r and heighth, and a hemispherical top. The tank is to be constructed to hold 500 meter^3 of fluid when filled. The cost to construct the cylindrical part of the tank is $300 per square meter of the surface area; the hemispherical part costs $400 per square meter. Determine the radius that results in the least cost and compute the corresponding height and the cost using graphical approach. V your results using the calculus approach.Explanation / Answer
Given Total Capacity/Volume of the tank = 500 m3
Cylinderical part cost = 300/m2
Hemispherical part cost = 400/m2
Therefore , we can solve as
The surface area of cylindrical part = 2* pi* r* h
the surface area of hemispherical top = 2*pi*r2
Total_Vol = 500
Radius r = linspace(2, 10, 1000);
height h = (500 - ((2*pi*r.^3)/3))./(pi * (r.^2)); where (2*pi*r.^3)/3 is the volume of cylinderical part and (pi * (r.^2) is the volume of hemispherical top part
Total_Cost = (300*2*pi.*r.*h) + (400*2*pi*r2); where 2*pi.*r.*h -The surface area of cylindrical part and 2*pi*r2 -the surface area of hemispherical top
To determine minumum cost and correspondence radius
[Min_Cost, Index] = min(Total_Cost)
Min_r = r(Index)
Corresponding_h = h(Index)
plot(r,Total_Cost)
xlabel ('Radius (Meter)')
ylabel ('Cost ($)')
title ('Cost versus Radius').
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