A trough is 6 feet long and has ends that are isosceles triangles that are 1 foot high and 3.5 feet wide. If the trough is being filled at a rate of 9 cubic feet per minute, how fast is the height of the water increaseing when the height is 5 inches?

Answer 1

using similar triangles, we see that when the water is of height h, the width of the cross-section is

w = 3.5h

So, the volume of water at height h is

v = 1/2 6*h(3.5h) = 10.5h^2
so, we have

dv/dt = 21h dh/dt
Now just plug in your numbers and solve for dh/dt