Questions and Answers
A 20,000 m^3 rectangular cistern is to be made from reinforced concrete so that the interior length will be twice the height. If cost is $40/m^2 for base, $100/m^2 for side walls, and 200/m^2 for roof, find the interior dimensions( to one decimal place) that will keep the cost to a minimum. To protect the water table, the building code specifies that no excavation can be more than 22 m deep. It also specifies that all cisterns must be at least 1 m in depth. Please help, really need this.
Building code limits: 1 ≤ h ≤ 22
If h = height, then 2h is the length. If the volume is 20,000, then the width is 20000/2h² or 1000/h².
The area of the base or roof is 2h * 1000/h² or 2000/h m².
The area of the walls is the perimeter of the base times the height. The perimeter is 2(L + W) or 2(2h + 1000/h²) or 4h + 2000/h². The area of the walls is h(4h + 2000/h²) m².
If Y is the total cost, then Y = price * floor + price * walls + price * ceiling.
Y = 40(2000/h) + 100(h(4h + 2000/h²)) + 200(2000/h)
In the calculator, enter:
y1 = 40(2000/x) + 100(x(4x + 2000/x²)) + 200(2000/x)
The height value that gives the minimum total price is when h = 9.5 m. The length is 18.9 m. The width is 11.1 m.
The minimum price is $107,678.05.
Height = 9.5 meters
length = 18.9 meters <==ANSWERS
width = 11.1 meters
I hope that helps!!
I am doing an estimate
I need a website or something that lists what was the cost for building a foundation was. Something of about 5060sq ft in flat slab foundation area with a footing foundation around it of about 2ft deep by 1.5 ft wide and reinforcing steel bars in it. The flat slab is about 8 in thick.
You might estimate between $5 and $20 per square foot, depending on your specific requirements. The type of concrete you need, the difficulty in excavation, anchoring, poured and formed features, welding and tie requirements, and so on will all change the price.
According to the references below, a good estimate for concrete is about $70 per cubic yard. You can use the calculator in the reference to estimate your yardage, and get a better ballpark figure. Note that the calculator requests several parameters which you haven't specified in your question, so maybe you'll need to do some more research.
All work is calculated by cubic yards of concrete, and other factors like any excavation, do you want wire mesh in the concrete. Do you want 2500 psi, 3000psi etc. You say it is a crawl space, is it big enough for someone to get under and work, pouring and finishing. You need to take these things into consideration when you get an estimate. It is impossible to even get a ballpark here. There is a tool that you can use to get an idea how much concrete you will need, and if you are doing it yourself this will help. A contractor will use their own estimate.