[binkgle]

An oil storage tank has the shape of a solid obtained by revolving the curve y= x 9
625
4 from
x = 0 to x = 5 about the y-axis, where x and y are measured in feet. Oil weighing 50 pounds
per cubic foot flowed into an initially empty tank at a constant rate of 8 cubic feet per minute. When
the depth of the oil reached 6 feet, the flow stopped. (Note: y = 9 when x = 5.)
(a) Let h be the depth, in feet, of the oil in the tank. How fast was the depth of the oil in the tank
increasing when h = 4? Indicate units of measure.
(b) Find, to the nearest foot-pound, the amount of work required to empty the tank by pumping
all of the oil back to the top of the tank.



I've no idea even where to start. I've been looking over the models we went through in class, but this doesn't really go with any of them.

 

[Firam]

What is the function for the size of the tank? I get the bounds are 0 to 5 but confused what you are trying to say with the:

y= x 9
625
4

 

[binkgle]

oops, i copied the problem from an online copy and i guess that didn't work so well. it's

y= (9/625)*x^4

 

[CSMR]

Quote:

Originally Posted by binkgle /img/forum/go_quote.gif (a) Let h be the depth, in feet, of the oil in the tank. How fast was the depth of the oil in the tank increasing when h = 4? Indicate units of measure.

Can you do this part? Do you have any ideas?
For the depth to increase by dh, how much volume must be added approximately? How much time does this take?
Quote:

(b) Find, to the nearest foot-pound, the amount of work required to empty the tank by pumping all of the oil back to the top of the tank.

Try thinking in this way: divide the tank into slices of height dh. How much energy does it take to move each slice to the top? What is the total energy? Now write as an integral.

Of course you can use next to no energy if you want to get the oil onto the ground. I assume the oil is all going to one level - the top of the tank.
Quote:

I've no idea even where to start. I've been looking over the models we went through in class, but this doesn't really go with any of them.

That's excellent because you don't learn much by regurgitating methods.

 

[binkgle]

problem solved. thank you