How Fast Does the Water Level Rise in a Triangular Trough?

[decamij]

Water is being pumped into a trough that is 4.5m long and has a cross section in the shape of an equilateral triangle 1.5m on a side. If the rate of inflow is 2m3/min, how fast is the water level rising when the water is 0.5m deep?

Answer is 0.77m/min.

Sorry for not posting this in the homework help section - saw the sign afterwards, and don't really have much time to move it.

 

[HallsofIvy]

Another point is that you should show us what you have already tried- don't just post the problem!

 

[Sick0Fant]

Well, I can try to help you, but I don't have enough time to work it out.

You want to find the rate of change of the area, so you'll need to use

a=1/2bh

Then eventually differentiate.

You should use properties of similar triangles to solve for the unknown.

then,
da/dt=(1/2)bh*(db/dt)

and you should be able to know all those variables.

Or else I'm completely wrong

 

[decamij]

But its a triangular prism, isn't it? I don't think just using area will work. I did this:

I use the equilateral triangle to find the height of the prism, and used the equation:

V = 1/2lwh (where l is 4.5, height is 1.5, and width was solved in terms of h).
= 1/2lo.58h^2, (er something like that)
I tried differentiating the equation to get:
dv/dt = 1.16h(dh/dt) --> (i think)


My final answer was 0.75m/min