Question

the conical tank with radius 5 feet and height 10 feet is filled to within 2 feet of the top of olive oil weighing 57lbs per cubic foot. how much work does it take to pump the oil to the rim of the tank?

Answer 1

i don't know the answer but i want to know if i setup the equation right.
\[57*25\pi \int\limits_{0}^{8}(10-y)dy\]

Answer 2

actually i got \[57\pi/4\int\limits_{0}^{8}(y^2-20y+100)(y-10)dy\]

Answer 3

but my answer came out to be negative number

Answer 4

what are you learning?



if you add the shown incremental amount of mass into a cone, you can say that the increase in the potential energy (dU) of the system is: \(dU = \rho \; \pi r^2 \; dz\). where \(\rho\) is the fluid's density.

and that is the work done.

in your case, \(r = \frac{z}{2}\) and vice versa.

so you should be able to build a nice little integral.

does that ring a bell?