SOLUTION: A steel storage tank for propane gas is to be constructed in the shape of a right cylinder with a hemisphere at each end. the construction cost per square foot of the end pieces is
Algebra.Com
Question 95073: A steel storage tank for propane gas is to be constructed in the shape of a right cylinder with a hemisphere at each end. the construction cost per square foot of the end pieces is $4.00, while the cylindrical part costs $2.00 per square foot. If the tank needs to hold 10(pi symbol)ft^3 of propane gas, what dimensions minimize the cost of construction? What is the minimum cost?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A steel storage tank for propane gas is to be constructed in the shape of a right cylinder with a hemisphere at each end. the construction cost per square foot of the end pieces is $4.00, while the cylindrical part costs $2.00 per square foot. If the tank needs to hold 10(pi symbol)ft^3 of propane gas, what dimensions minimize the cost of construction? What is the minimum cost?
-------------------
Let the radius be "x" feet.
Area of the combined semi-circular end pieces = 4pir^2 = 4(pi)x^2
Volume of the combined semi-circular end pieces = (4/3)(pi)x^3
------------
Area of the cylindrical part = 2(pi)xh
Volume of the cylindrical part = (pi)x^2h
----------------
EQUATION:
volumn + volumn = volumn
(4/3)(pi)x^3 + (pi)x^2h = 10(pi)
(4/3)x^3 + x^2h - 10 = 0
Comment: Not knowing "h" results in not knowing "x".
----------------
Price equation:
price + price = total price
4[4(pi)x^2] + 2[2(pi)xh] = total price
Comment: Not knowing "h" results in not being able to find the minimum here.
================
Cheers,
Stan H.
RELATED QUESTIONS
A propane gas tank is in the shape of a right circular cylinder with a hemisphere at each (answered by ankor@dixie-net.com)
A propane gas tank has the shape of a right circular cylinder with a hemisphere on each... (answered by Alan3354)
A propane gas tank consists of a cylinder with a hemisphere at each end. Find the volume... (answered by Alan3354)
A propane tank is in the form of a cylinder with two half-spheres, one on each end. The... (answered by nerdybill,Alan3354)
hi. can you help me to solve this problem.? thanks a lot
A propane tank is constructed... (answered by solver91311)
((Formulas involved are: Surface area=2nrh ; Volume=1/3lbh ; Surface area=4nr^2 and... (answered by solver91311)
A large grain silo is to be constructed in the shape of a circular cylinder with a... (answered by mananth)
A large grain silo is to be constructed in the shape of a circular cylinder with a... (answered by Jc0110)
A large grain silo is to be constructed in the shape of a circular cylinder with a... (answered by ankor@dixie-net.com)