Show sufficient supporting work for all problems below. 1) A 20 ft cylindrical tank is leaking water at a rate of 3 ft/sec and forming a circular puddle. The radius of the tank is 8 ft. Answer each of the questions below. a) Find the rate at which the height of the water is changing at the moment the height is 5 ft.. b) If the radius of the puddle is growing at a rate that is 1/3 of the rate at which water is leaking from the tank, find the rate at which the area of the puddle is changing at the moment that the radius of the puddle is 7 ft. 2) A conical pile of gravel has a radius that is four times its height. If gravel is being poured into the pile at a rate of 35 ft/min, find the rate at which the height of the pile is changing at the moment that the radius is 30 ft. (Can you find the two equations to use in this problem?) autop nonoga alshsV bus ease phemun) anoton abonoya gon 3) A conical tank with height 20 m and radius 5 m is being filled with a liquid. The height is increasing at a rate of 0.4 m/min. Find the rate at which the volume is changing when the radius is 2 m. (Use the concept of similar triangles.)