Question

A vertical right circular cylindrical tank measures high and diameter. It is full of oil weighing . How much work does it take to pump the oil to the level of the top of the tank? Give your answer to the nearest ft ∙ lb.

Answer 1

Work = force * distance. So in this case, we're interested in how much the oil weighs and how far it gets lifted or pumped out of the tank.

Answer 2

yes.

Answer 3

So I would take the cross section of the tank first. That would just be the area. Multiply that by the weight.

Answer 4

Then multiply that buy the distance from the top of the tank. Which would be a variable ranging from 0 to H, with H being the height.

Answer 5

yes.

Answer 6

Integral from 0 to H{PI*radius^2 * weight* x^2}dx

Answer 7

I thiiink. Not certain about the x^2, but I believe that's correct. Because the cross section times the height gives the volume. And then it's multiplied by the weight. Then it's multiplied by the height.

Answer 8

so x is height, or distance from the top of the tank.

Answer 9

what i did is: F=601pi(-y2+14x)
W=601pi(-y2+14y)(14-y)
is this true? my answer is not the same as instructor.

Answer 10

F is force...
What are those numbers and what do the variable stand for? y looks like height? What is x?

Answer 11

yes, F is force =weight . volume .
that is not x i mean y
is this wrong?

Answer 12

What is the radius of the container?

Answer 13

A vertical right circular cylindrical tank measures 26 high and 14 diameter. It is full of oil weighing 601 . How much work does it take to pump the oil to the level of the top of the tank? Give your answer to the nearest ft ∙ lb.

Answer 14

"what i did is:
F=601pi(-y2+14x)
W=601pi(-y2+14y)(14-y)"
601 is total weight. You need to start with weight per unit volume. Otherwise you're counting all the weight at the top.

Answer 15

And then there should be an r^2 in there, so 7^2.

Answer 16

W=601pi(-y2+14y)(14-y) this is the same as what i did, is it correct? where r u going to use r^2 or 7^2 ?

Answer 17

Okay. Here's what I'm thinking.
Force = volume * (weight/ volume)
volume at a particular height is pi*r^2*y = pi*7^2*y
weight/volume = 601/volume = 601/(pi*7^2*height) = 601/(pi*7^2*26)