Name A gas tank has the shape of an elliptical cylinder whose major axis n feet and minor axis radius r is 4 feet as shown in the figure to t the depth of the gas in the tank, where h is a function of time t, measured in minutes. The volume V of the gas in the tank is changing at the rate of-8 / cubic inches per minute. (The volume V of an elliptical cylinder with major R, minor radius r and height h is given by v-? Rh. radius R is 6 the right. Let h be radius a)Show that dir = (3pts) di 3 for h as a function of 0, solve the differential equation 0, solve the differential equationdhforas a function of t. (5 ps) b) Given that h 27 at time c) How long does the gas tank take to empty? (1 pt)

AP Calculus - Growth AP Type (Chapter 41-42) Name A gas tank has the shape of an elliptical cylinder whose major axis radius R is 6 R = 6 in feet and minor axis radius r is 4 feet as shown in the figure to the right. Let h be r = 4 in, he depth of the gas in the tank, where h is a function of time t, measured in minutes. The volume V of the gas in the tank is changing at the rate of -8nt(h) cubic inches per minute. (The volume V of an elliptical cylinder with major radius R, minor radius r and height h is given by V = ARh . h a) Show that an dh _Jh dt 3 . (3 pts) b) Given that h = 27 at time t = 0, solve the differential equation dh _Uh for h as a function of t. (5 pts) dt 3 w long does the gas tank take to empty? (1 pt)