Question

A trough is 16 ft long and its ends have the shape of isosceles triangles that are 4 ft across at the top and have a height of 1 ft. If the trough is being filled with water at a rate of 9 ft3/min, how fast is the water level rising when the water is 5 inches deep?

Answer 1

how do i go about solving the problem?

Answer 2

\[V=16 x^2 \text{Cot}\left[\text{ArcTan}\left[\frac{1}{2}\right]\right]=32x^2 \]Take the total derivative of the above and solve for dx.\[\text{dx}\text{ =}\frac{\text{dV}}{64 x}=\frac{9}{64*\frac{5}{12}}=\frac{27}{80 } \text{ft}/\min\]