A trough is 10ft long and its ends have the shape of isoceles triangles that are 3ft across at the top and have a height of 1ft. Suppose the trough is being filled with water at a rate of 12ft3/min.
(a) Let, V (t) be the volume in trough in ft3 at time t minutes. Give a formula for V (t) in terms of h(t) where h(t) is height of the water in the trough in ft at time t minutes.
(b) Use your formula for V (t) and h(t) to find how fast the water level is rising when height of the water is .75ft. (that is, relate the rate of change of volume to the rate of change of height)