1. ## Depth

A trough is 12 feet long and 3 feet across the top (see figure). Its ends are isosceles triangles with altitudes of 3 feet.
(a) If water is being pumped into the trough at 2 cubic feet per minute, how fast is the water level rising when h is 1.3 foot deep?

_________ ft/min
(b) If the water is rising at a rate of inch per minute when h = 2.1, determine the rate at which water is being pumped into the trough.

_________ ft3/min

A trough is 12 feet long and 3 feet across the top (see figure). Its ends are isosceles triangles with altitudes of 3 feet.
(a) If water is being pumped into the trough at 2 cubic feet per minute, how fast is the water level rising when h is 1.3 foot deep?

_________ ft/min
(b) If the water is rising at a rate of inch per minute when h = 2.1, determine the rate at which water is being pumped into the trough.

_________ ft3/min
you need to get the volume, V, of water in the trough as a function of its depth, h.

$\displaystyle V$ = (area of end triangle)(trough length)

$\displaystyle V = \frac{1}{2}bh \cdot 12 = 6bh$

note from the figure that $\displaystyle b = h$ ...

$\displaystyle V = 6h^2$

take the time derivative and answer the questions.