Question

A water trough is 10m long and a cross-section has the shape of an isosceles trapezoid that is 30cm wide at the bottom, 80cm wide at the top, and has height 50cm. If the trough is being filled with water at a rate of .2m3/min, how fast is the water level rising when the water is 30cm deep?

______________ m/min

Answer 1

hey @pitamar sorry for bothering you again but do you know how to solve this one? it's ok if you're busy though

Answer 2

Ok, I'm back. sorry

Answer 3

it's okay

Answer 4

ok, so basically we know that the water are filled in a constant rate of \(0.2_{m^3/min}\)
Notice that \(m^3\) is a unit of volume (normally the density of water wouldn't change, so it also tells us the mass, but nevermind that)
So we know that the volume of the water inside the trough grows constantly. Now what we want to find is the rate of change in the 'depth' of the water.

Look here:
http://www.onlineconversion.com/images/object_volume_trapezoid.png

We're looking for the rate of change in \(h_1\). Ok so far?

Answer 5

ok

Answer 6

Ok, so first let's try and make a function that will tell us the volume of the water for a given depth. ok?
That basically means you want to make a function for the volume of the trough from the bottom and up to some height above the bottom.
Can do?

Answer 7

i'm not sure but are you supposed to do the area of the end times the depth?

Answer 8

let me ask you this, what will be the shape of the water inside the trough?

Answer 9

trapezoid prismish? idk

Answer 10

well, yes. exactly =)
and what is the volume of a prism?