1. Water flows into a vertical cylindrical tank at the rate of 12 cu.ft/min. The surface rises 6 inches per minute. Find the radius of the tank.
2. If the angle of elevation of the sun is 45degrees and is decreasing at 0.25rad/hour, how fast is the shadow cast on level ground changing(lengthening) when the pole is 50ft tall?
V=pi (r^2) h --> is used this as my working equation
dV/dt = 2pir(dr/dt)(dh/dt)
..i stopped in here because it noticed that there is no rate for radius, so what I did is to work again..
r= sqrt.(V/pi h) --> this is my another working equation
r = sqrt[ (dV/dt)/ pi (dh/dt) ]
r = 2.76 ft
There it goes.. I don't know if it is correct.
tan 45 = 50/x
x = 50/tan45 --> this serves as my working equation
dx/dt = [-50sec^2 (45) (0.25rad/hr)] / tan^2 (45)
dx/dt = -25ft/hr
There is all my effort. Tell me all the corrections.