TIME RATES

TIME RATES

Problem:

      1.       A rectangular bin measures 5 meters long and 3 meters wide. How fast will the surface rises if water flows inside rates at 10 ft³/min.

Required:  dh/dt

Solution: 

V = L * W * H

Where:  V = volume

                L = length

               W = width

                H = height

V = LWH (substitute length and width)

V = 5 m * 3 m * H

dv/dt = 30 dH/dt

10 = 30 dH/dt

dH/dt = 0.33 m/min. (answer)

2.       Water from the faucet fills the tank in vertical cylinder in shape at 20 ft³/min in rate. The radius of the tank is 3.5 ft. How fast will the surface of water rises

Required:  dh/dt

Solution: 

V = π * r² *h

Where:  V = volume

                π = pi

                r = radius

                h = height

V = LWH (substitute the radius)

V = π * r² *h

V = π * (3.5)² *h

V = 12.25π h

dV/dt = 12.25 π dh/dt

20 = 12.25 π dh/dt

dh/dt = 20/12.25 * π

dh/dt= 1.632 π ft/min. (answer)