Question

A trough is 14 ft long and its ends have the shape of isosceles triangles that are 2 ft across at the top and have a height of 1 ft. If the trough is being filled with water at a rate of 8 ft3/min, how fast is the water level rising when the water is 9 inches deep?

Answer 1

hello

Answer 2

let x be length of water filled from bottem.
so length of water surface at cross section =2x(using similar triangle)
now volume of water filled V=(1/2)(x)(2x).14=14x^2
dV/dx=28x
(dV/dt).(dt/dx)=28x
dt/dx=28x.(dt/dV)
now put the values from question
dt/dx=28(9/12).1/8
dx/dt=24/63.
ans .... water level increases at the rate of 24/63 ft /min

Answer 3

Thanks