FLOWING WATER
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)
