Answer:
number of minutes to drain the entire tower = 241 minutes(nearest minutes)
Step-by-step explanation:
The water tower has the shape of a cylinder with a cone on top . The volume of the water tower can be find when you find the sum of the volume of the cylinder and the cone.
Therefore,
volume of the cylinder = πr²h
where
r = 12/2 = 6 ft
h = 15 ft
volume = π × 6² × 15
volume = π × 36 × 15
volume of the cylinder = 540π
Volume of the cone = 1/3πr²h
r = 6 ft
Using tangential ratio we can find the height which is the opposite side of the triangle
tan 25° = opposite/adjacent
tan 25° = h/6
cross multiply
h = 6 tan 25°
h = 6 × 0.46630765815
h = 2.79784594893
h = 2.8 ft
volume of the cone = 1/3πr²h
volume = 1/3 × π × 36 × 2.8
volume = 100.8π/3
volume = 33.6π
Volume of the tower system = 540π + 33.6π = 573.6π
volume of the tower system = 573.6 × 3.14 = 1801.104 ft³
1 cubic ft = 7.48 gallons
1801.104 cubic fit = ? gallons
cross multiply
gallons = 1801.104 × 7.48
gallons = 13472.25792 gallons
The residents drains the water at the rate of 56 gallons per minute. Therefore,
56 gallons = 1 minutes
13472.25792 gallons = ? minutes
number of minutes = 13472.25792 /56
number of minutes = 240.576034286
number of minutes to drain the entire tower = 241 minutes(nearest minutes)
