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?

My Effort..

1.

Sol'n:

V=Bh

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..

V=Bh

V=pi (r^2)h

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.

2.

Sol'n:

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.

Thanks!