Question

Find the work in ft-lbs required to empty a full hemispherical tank with a radius of 4 ft, by pumping water to the top of the tank.

please help? its just a curiosity question, way above my own lvl, so really simple english would be nice xP

Answer 1

@jdoe0001 @Loser66 @thomaster @Hero @tkhunny could any of u help or know someone that could help :3

Answer 2

I'm on the app so I can't even bump >.<

Answer 3

@Hero do u have any idea? :/

Answer 4

The Work Formula For Emptying A Tank is:

\[\text{Work} = D \int_{a}^{b}A(y)[H - y]dy\] where
\(D\) is the Density
\(A(y)\) is the cross sectional area
\(H\) is the height

Answer 5

alright, that makes sense so far, but I'm slightly confused on how to get the A(y)

Answer 6

it has something to do with radius i think

Answer 7

yeah xD it might be the area of a circle formula, since you r taking an infinite number of thin slices of circles from the hemisphere?
but idk how that would work in this case?

Answer 8

@Hero so would it be something like
9810pi times integral from -4 to 0 of (16-x^2)(-x) dx ? :/

Answer 9

@FibonacciChick666

Answer 10

A(y) is the area of the thing, so what is half of the area of the basin?

Answer 11

not half, just area

Answer 12

32pi ?
cuz volume of sphere is 4 pi r^2

Answer 13

or 64pi :/

Answer 14

...well this is confusing as heck to me...
but i'll try o.e

Answer 15

ok what did you need, jeff?

Answer 16

helping answering this

Answer 17

ok, hold on

Answer 18

W = ∫ F · ds
= 62.4 π ∫ (8-y) (36 - (6-y)²) dy [0,6] ............ water = 62.4 lbs/ft³
= (62.4 π) y²/12 (3y² - 80y + 576) ...... from 0 to 6
= (62.4 π) 3 (108 - 480 + 576)
= 62.4 π (612)
≈ 119973.6535 ft-lbs

Answer: ≈ 119973.6535 ft-lbs

(not sure is this is the right one... or not)

Answer 19

yea something like that

Answer 20

where'd u get those numbers from???
all they gave was a radius of 4

Answer 21

like i said... (not sure is this is the right one... or not)

Answer 22

im not sure i understand this too well

Answer 23

me either o-o
mathematical equations r my arch enemies...

Answer 24

right?

Answer 25

well, thanks for trying at least :)

Answer 26

Yeah- no probs xD

Answer 27

it's wrong because i think it has to have a pi in it

Answer 28

OMG thank you hero! <3

Answer 29

he multiplied by pi in the last step, look at the step before, jeff

Answer 30

sry I don't get it jiggles so sry I just don't now so here a medal for it

Answer 31

that final answer is not it

Answer 32

@jeffsours, if you have a better solution post it.

Answer 33

i don't but i texted teacher's hotline it's not it and its confusing me.

Answer 34

so how ya guys doing

Answer 35

If you haven't performed the steps yourself how do you know what is right and what isn't?

Answer 36

The second to last step is written in pi format.

Answer 37

can you stop spammers pls hero

Answer 38

I told ya to look at the step before the last, jeff
62.4 times 64 times pi -> 3993.6pi

Answer 39

so it's 3993.6 pi?

Answer 40

I did a full read, there were no mistakes in hero's work

Answer 41

yes...

Answer 42

did you even look through the work jeff? hero worked hard to write it out for us, try to read it carefully

Answer 43

i did and i'm not getting it but it seems right

Answer 44

yes. all throughout D = 64
which he plugged in in the second to last step and there was a pi next to it.

Answer 45

what no, I was saying 64pi was in it, not that it was the answer.

Answer 46

it should be 3993.6pi

Answer 47

yea its correct you guys I found the answer on a website on http://mathehelp.com

Answer 48

omg hero i'm not a troll he made it 4000pi now please unban my other account

Answer 49

I would like to apologize for any inconveniences from my asking this question. I had been genuinely interested in learning and understanding how to answer such question myself, so thank you @Hero for helping with the step by step and helping me gain a better understanding of the type of thinking required to get through a problem like this in the future, thank you.

Answer 50

i apologize also