Water Tank

How do I solve this? I have tried it many times but i just don't get it. please help!

A cylindrical tank with a hemispherical top is to be constructed that will hold 5.00x105L when filled. Determine the tank radius R and height H to minimize the tank cost if the cylindrical portion costs $300/m2 of surface area and the hemispherical portion costs $400/m2.

Mathematical model:
Cylinder volume Vc= pi*R^H
Hemisphere volume Vh= (2/3)*pi*R^3
cylinder area ac= 2*pi*R*H
hemisphere surface area ah= 2*pi*R^2

Assumptions:
Tank contains no dead air space, Concrete slab with hermetic seal is provided for the base. Cost of the base does not change appreciably with tank dimensions.

Computational method:
Express total volume in meters cubed (noted:1m3=1000L) as a function of height and radius.

Vtank= Vc+Vh

For Vtank= 5x 10^5L= 500m3
500= pi*R^2*H + (2/3)*pi*R^3

Solving for H: H= (500/pi*R^2) - (2*R/3)

Cost in dollars as a function of height and radius
C= 300Ac + 400Ah = 300(2piRH) +400(2piR^2)

Method: compute H and then C for a range of values of R, then find the minimum value of C and the corresponding values of R and H.
To determine the range of R to investigate, make an approximation by assuming that H=R:

Then from the tank volume:
Vtank= 500 = piR^3 + (2/3)piR^3 = (5/3)piR^3

R in the range 3.0 to 7.0 meters.

2nd) Plot y=cos sin red and z= 1- (x2/2)+ (x4/24) in blue for 0<x<pi on the same plot.

[Walter Roberson]

http://www.mathworks.com/matlabcentral/answers/6200-tutorial-how-to-ask-a-question-on-answers-and-get-a-fast-answer

Answer 1

[Paul]

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