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

Algebra ->  Surface-area -> 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       Log On


   

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(32388) About Me  (Show Source):
You can put this solution on YOUR website!
For a cylindrical room, h is height, r is the radius.
V+=+%28pi%29r%5E2h Volume of the cylinder
S+=+2%28pi%29r%5E2%2B2%28pi%29rh Surface area of top and bottom plus unrolled side
V=20000=%28pi%29r%5E2h
You can rearrange the equation to solve for h as a function of r.
h=20000%2F%28%28pi%29r%5E2%29
Then substitute that back into the surface area equation,
S+=+2%28pi%29r%5E2%2B2%28pi%29rh
S+=+2%28pi%29r%5E2%2B2%28pi%29r%2820000%2F%28%28pi%29r%5E2%29%29
S+=+2%28pi%29r%5E2%2B40000%2Fr
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.
h=20000%2F%28%28pi%29r%5E2%29
h=20000%2F%28%28pi%2915.1%5E2%29
h=27.9%29
Make sure to check your answer.
V+=+%28pi%29r%5E2h
V+=+%28pi%2915.1%5E2%2A27.9
V+=+19985
Close enough.
r=15.1 m, h=27.9 m