Tutorial Exercise A trough is 12 it long and its ends have the shape of isosceles triangles that are 3 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 ft / min, how fast is the water level rising when the water is 6 inches deep? Step 1 Let h be the water's height and b be the distance across the top of the water. Using the diagram below, find the relation between b and h. Step 2 The volume of the water is as follows. V = =bhi 1bh 12 12 = 6 0 6 (3h) (h) 18h 1842 Step 3 We must find dh/dt. We have 8 = 24 = 36/ 36h Step 4 In feet, we know that h = 6/12 1/2 ft. Step 5 Consequently, we can conclude the following. oh = 7/6 x ft/min Submit Skip (you cannot come back)