SOLUTION: hI1 please help me with this. I have done so many questions before but this one just doesnt give the right answer?? any help would be apreciated The volume of a library is

Question 117465: hI1
please help me with this. I have done so many questions before but this one just doesnt give the right answer?? any help would be apreciated

The volume of a library is 20000 m (cubed) We have to minimize the Surface area to ignore the heat loss.Dtermine the dimensions of the building that will best give us teh minimum Surface area.??
thanks for any help coming this way.
Answer by Fombitz(13823) (Show Source):
You can put this solution on YOUR website!
For a cylindrical room, h is height, r is the radius.
Volume of the cylinder
Surface area of top and bottom plus unrolled side

You can rearrange the equation to solve for h as a function of r.

Then substitute that back into the surface area equation,

Plot S using various values of r and look for a minimum.
8.1, 5350.
9.1, 4915.
10.1, 4601.
11.1, 4377.
12.1, 4225.
13.1, 4131.
14.1, 4085.
15.1, 4080.
16.1, 4112.
17.1, 4175.
18.1, 4267.
19.1, 4385.
20.1, 4527.
Looks like a minimum at r=15.1.
Now that you have r, go back to your equation for h and solve.

Make sure to check your answer.

Close enough.
r=15.1 m, h=27.9 m