calculating work

[mark]

a cylindrical reservoir is 30 ft in diameter and 100 ft deep. if the rservoir is filled to a depth of 60 ft, how much work is required to pump all the water to a level which is 10 ft above the reservoir.

here is my work

------------ - 100 ft
- -
- -
- ---------- - 60 ft
- -
-----------

w = weight *distance

weight = rolls pie r^2

distance = i cant figure out what the distance is

r = 15

intergral from 60 to 110 rolls pie r^2 (distance)

 

[soroban]

Hello, mark!

A cylindrical reservoir is 30 ft in diameter and 100 ft deep.
If the reservoir is filled to a depth of 60 ft, how much work is required
to pump all the water to a level which is 10 ft above the reservoir.

Here is my work

            ------------  - 100 ft
            -          -
            -          -
            ------------  60 ft
            -          -
            ------------

w = weight *distance

weight = rolls pie r^2 . . . what is "rolls"? density?

distance = i cant figure out what the distance is

r = 15

intergral from 60 to 110 rolls pie r^2 (distance)
No, your limits are above the water.

     110       ---      -
                ↑       :
                ↑       :
     100  *-----↑-----* :
        : |     ↑     | 110-y
        : |     ↑     | :
       60 | - - ↑ - - | :
        : |:::::↑:::::| :
        : |===========| -
        : |:::::::::::| :
        : |:::::::::::| y
        : |:::::::::::| :
        - *-----------* -

\(\displaystyle \L W\;=\;225\pi\rho\int^{\;\;\;\:60}_0(110\,-\,y)\,dy\)

 

[mark]

thank you so much for your help, i understand it now