Question

A reservoir shaped like a right circular cone, point down, 20ft across the top and 8ft deep is filled to a depth of 5 feet. Water is to be pumped to the same level as the top. How much work does it take?

Answer 1

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Answer 2

density of water is 62.4 right?

Answer 3

yes

Answer 4

so
you get your force

Answer 5

can you tell me alittle about work? (i'm low on this knowledge)
i know it equals force times distance
but i don't see how to get force here?

Answer 6

which will be 62.4 then you times it by 10/8y

Answer 7

annon can you tell me how to get those two terms?

Answer 8

ya the 62.4 is given or known, and you set the cone on a 2D graph

Answer 9

the slope is y=8/10
make it x=10/8y since you need the y component

Answer 10

oh ok density of water is always 62.4 ok got it

Answer 11

multiply them

Answer 12

you're so smart
i don't understand work at all
it must be a physics/engineer thing

Answer 13

i am a mech engineering major :)

Answer 14

i was math major

Answer 15

work = (6240/64)pi integral from 0 to 10 of y^3 dy

Answer 16

did u get it mdntjem?

Answer 17

I have a question, how did you get the limits of integration from 0 to 10?

Answer 18

well you have to pump from bottom to top right?

Answer 19

yes

Answer 20

thats how limits of integration is where it begins to where it en

Answer 21

I thought it would be to 8

Answer 22

it would 8 if they said to stop at 8

Answer 23

thats how limits of integration is where it begins to where it en

Answer 24

Is it because the cone is parallel to the y-axis and the upper limit needs to be the top line perpendicular to the y-axis?

Answer 25

if you look at the cone from a side veiw

Answer 26

oh wait, ur right 0 to 8

Answer 27

sorry lol and my numbers are wrong give me a sec.

Answer 28

Okay :) no prob

Answer 29

sorry about that :)

Answer 30

62.4(400/64)*pi integral from 0 to 8 of y^3 dy

Answer 31

Not a problem

Answer 32

this should be the right answer after you integrate it out

Answer 33

I have another quick question, how'd you get the (400/64)?

Answer 34

if you look at the cone from the side, it makes a right triangle on a graph and it starts at zero and slopes up 8 and over 20

Answer 35

so your equation is y=(8/20) x

Answer 36

since you need it in terms of x to be your radius, you solve for x,
x= (20/8)y

Answer 37

now you use this as your "r" for the formula of the volume.

Answer 38

pi*r^2

Answer 39

so...
pi* ((20/8)y)^2

Answer 40

so you get pi* (20^2 / 8^2) y^2

Answer 41

Oh I see!

Answer 42

:D i hope i was clear enough

Answer 43

I was doing mine with 10/8, so I got 5/4x=r

Answer 44

oh i did that too at first until i realised it was a right conical tank

Answer 45

Okay, I get it now. Thank you for all your help!

Answer 46

np :)