SOLUTION: A tank is to be constructed that will hold 5.00 X 10^5L when filled. The Shape is to be cylindrical with a hemispherical top. find the dimensions of the container (that has a volum

Algebra ->  Volume -> SOLUTION: A tank is to be constructed that will hold 5.00 X 10^5L when filled. The Shape is to be cylindrical with a hemispherical top. find the dimensions of the container (that has a volum      Log On


   

Question 347119: A tank is to be constructed that will hold 5.00 X 10^5L when filled. The Shape is to be cylindrical with a hemispherical top. find the dimensions of the container (that has a volume of 500000 liters) so you can calculate the surface area.
No diameter or height given, you must find the height and diamter based on the 500,000L and no dead air space.
Tank has no dead air space
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
A tank is to be constructed that will hold 5.00 X 10^5L when filled. The Shape is to be cylindrical with a hemispherical top. find the dimensions of the container (that has a volume of 500000 liters) so you can calculate the surface area.
-------------
h = height of the cylinder
r = radius of the cylinder and of the hemisphere
-------------------------------
-----Cyl vol + Hemisph vol
Vol+=+pi%2Ar%5E2%2Ah+%2B+2%2Api%2Ar%5E3%2F3+=+500000
500000+=+pi%2Ar%5E2%2A%28h+%2B+2r%2F3%29
500000%2F%28pi%2Ar%5E2%29+=+h+%2B+2r%2F3
h+=+500000%2F%28pi%2Ar%5E2%29+-+2r%2F3
-------------------
SA+=+2pi%2Ar%2Ah+%2B+2pir%5E2
SA+=+2pi%2Ar%2A%28500000%2F%28pi%2Ar%5E2%29+-+2r%2F3%29+%2B+2pi%2Ar%5E2
SA+=+1000000%2Fr+-+4pi%2Ar%5E2%2F3+%2B+2pi%2Ar%5E2
That's the surface area in terms of r. No numerical value of SA can be determined without a value of r. (The bottom is not included, btw)
---------------------
If you want the value of r that gives the minimum SA for the given shape and volume, that can be determined.