Difficult word problem. Can anyone solve this problem?

Question

A tank is in the shape of a right circular cone of altitude 20 feet and base radius 10 feet with its vertex at the ground. (Think of an ice cream cone with its point facing down.) The tank is externally braced to prevent its falling over. If the tank is full of a fluid which weighs 40 pounds per cubic foot, find the work done, in foot pounds, correct to the nearest hundred footpounds, in pumping all of the fluid out of the top of the tank.

possible homework solutions...

a. 294,500

b. 353,400

c. 418,900

d. 795,200

e. 1,178,100

f. 1,656,700

g. 2,650,700

h. 3,272,500

i. 3,769,900

or is it none of these ?

Answer 1

I'm not doing your homework for you.

Answer 2

Well, work is force * distance. Start off graphing the triangle that corresponds to the cone in two dimensions with the vertex on the origin. Next, write an equation for the line going from the vertex to the top in quadrant I. This will give you y=2x. Now, solve that for x, giving you x= 1/2 y. This will give you the radius of the circular shape (actually a cylinder with infinitesimal depth) in terms of the height. That was the hard part, now you have to put that together with the other parts.

If work is force * distance and force is volume * weight, then, you will use: volume * weight * distance; but this must all be in terms of the same variable.... as I am assuming this is a cal I problem. If you set your graph up like I explained, your height will be 20 - y, your weight is given, and the volume of each slice will be pi * r^2 where r is defined by the original equation of the line at height y.

So, putting it all together you would get:
volume________height___weight
pi (1/2 y)^2 dy___(20 - y)__40
then, integrate this from 0, the base, to 20, the top.

This is hardly a 'nasty' differential equation... in fact, I wouldn't call it a differential equation at all...

This gives you:
400000 pi / 5 which is roughly 418,900 ... so the answer is c!

Answer 3

The exact number would take some nasty differential equations but since all your possible answer are pretty spread out it should be easy to guess which one it is. Cone means the rate it will drain will increase as the radius decreases toward the bottom, the average height of the water during the entire draining process would be 3/4 height. So, find the volume of the cone (1/3*Pi*(10^2)*20) = 2094.4 cubic feet. Then find how far it has to go 20-(3/4)*20 = 5. Multiply those together and times 40 pounts per cubit foot and you get 418,880. And the answer is 418900.

Answer 4

That doesn't make sense. The cone can not have an altitude of 20 ft, and a base radius of 10 if this is a Right circular cone. The base radius has to be the same as the altitude. Right?

Answer 5

Correct answer is c, 418,879 ft-lb work.

Obtained by integrating Vol x density x distance that volume is raised. Vol is volume of an infinitesimally small slice of the cone; the volume of each slice is pi r squared dh. Radius r at any point along the height is expressed as r= 1/2 h.

No 'nasty differential equations' involved, just a single, simple integral straight from high school calculus.

Answer 6

It is not a word problem and it is a maths problem.

You need to compute the total volume of the fluid, find the center of gravity of the mass (it will be closer to the top) and then compute the work done to pump out the liquid over a height (which is 20 - the height of the centre of gravity from the ground).

Answer 7

C- statisticly C is correct most often in multiple choice. plus, if you multiply the transverse by the integer in the equation F= WMV/.577 you get something nowewhere near any of your answers.

Answer 8

I am not going to dignify this with any help (although I am pretty sure its easy, use an equation invloving pi and r^3 and l, multiply by 40, and see wot it says) because you are using non SI units, because your are American (I am guessing). Tut tut, using 'pound feet', Thats not a real unit.

Answer 9

My first decision could be...18 inches. My mom continuously informed me to bypass with my 1st instinct (decision), she'd say, "you will continuously be precise!" And ninety 8% of the time i'm. sturdy success!

Answer 10

E