# Homework Help: Rates of change

1. Mar 26, 2006

A trough is 10 ft long and its ends have the shape of isosceles triangles that are 3ft across at the top and have a height of 1ft. if the trough is filled with water at a rate of 12ft^3/min, how fast does teh water level rise when the water is 6inches deep?

so far i have: dv/dt= 12ft^3/min and need to find dh/dt.
V= base* height*length ? where length=10 ft.
what i don't understand is how come in my notes, the next step is that b becomes 0.5*b*h??

Last edited: Mar 26, 2006
2. Mar 26, 2006

### Integral

Staff Emeritus

The expression:

V= b*h*L

Gives the volume of a solid with a rectangular cross section. You have a solid with a triangular cross section so the the expression

V = .5*b*h*L

Would be correct.

can you complete the problem from there?

3. Mar 27, 2006

### HallsofIvy

V= base*height*length for a RECTANGULAR trough. This is TRIANGULAR. The area of a triangle is 0.5*b*h.

4. Apr 2, 2006