Mamta:
Here is where I got stuck - I kept searching for "triangle" - well .... a triangle is a 2 dimentional object.
So I though no - it was pyramid - but that was not exactly correct either, there is a formula specifically for troughs!! I just could not find it - and although the picture we drew was "kinda" ok - I think this one is better.

Troughs

Volume = (area of rectangle) (depth)

Volume = ((base * height)/2)*(length)

Trough example: = (area of triangle)(length)
= ((2ft X 3 ft)/2)(5 ft)

= (3 sq ft)(5 ft)
= 15 cu. ft.

Now we can apply this 's exampleinformation to our question:
A trough is 2 km long, and its ends are triangles with sides of length 1 meter, 1 meter and 1.2 meter.
Find the volume(V) of the water in the trough as a function of water level height(H)
The volume of the trough is a function of the height of the water

V = ½(base * height) * length

The volume of our triangle is ((1.2m X 1m)/2) (2m)

V = 1.2 sq meters that is when the trough is full
When h is 1m, V is 1.2sq meters
When h is 0, V is 0
So the range of h can be between 0 and 1 meters
And the range of V can be between 0 and 1.2 sq meters

If we were to graph this

This was the original drawing

I believe the drawing at the top of this page is what the
trough drawing should have looked like.

Thank you for taking the time to use eTutoring.org

I hope to see you on another Sunday very soon.

JilMac